Add hard3 subset and eq ids to released subsets
Browse files- README.md +26 -2
- data/hard.jsonl +200 -200
- data/hard1.jsonl +69 -69
- data/hard2.jsonl +200 -200
- data/hard3.jsonl +400 -0
- data/normal.jsonl +0 -0
- metadata/hard3.json +12 -0
README.md
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data_files:
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- split: train
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path: data/hard2.jsonl
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---
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# Equational Theories Selected Problems
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This dataset contains public training problem subsets selected from the Equational Theories Project raw implication dataset.
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This dataset is intended for Stage 1 of the Mathematics Distillation Challenge: Equational Theories competition.
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- `hard`: 200 selected problems co-curated by human mathematicians and AI, with 74 ground-truth `TRUE` labels and 126 ground-truth `FALSE` labels
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- `hard1`: a deduplicated version of the 200-problem `hard` subset, containing 69 unique problems total, with 24 ground-truth `TRUE` labels and 45 ground-truth `FALSE` labels
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- `hard2`: 200 selected problems co-curated by human mathematicians and AI, with 100 ground-truth `TRUE` labels and 100 ground-truth `FALSE` labels
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All subsets are public training problems and are exposed as the `train` split in this repository.
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Each record has the following fields:
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- `id`: stable identifier such as `normal_0001`, `hard_0001`, `hard1_0001`, or `
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- `index`: 1-based index within the subset
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- `difficulty`: `normal` or `hard`
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- `equation1`: Equation 1
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- `equation2`: Equation 2
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- `answer`: whether Equation 1 implies Equation 2 over all magmas
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- `derived_from`: parent subset name if the subset is derived from another subset
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- `notes`: optional explanatory notes
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Records in `hard1`
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## Usage
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"hard2",
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split="train",
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)
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```
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## Files
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- `data/hard.jsonl`
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- `data/hard1.jsonl`
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- `data/hard2.jsonl`
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- `metadata/normal.json`
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- `metadata/hard.json`
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- `metadata/hard1.json`
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- `metadata/hard2.json`
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data_files:
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- split: train
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path: data/hard2.jsonl
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- config_name: hard3
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data_files:
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- split: train
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path: data/hard3.jsonl
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---
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# Equational Theories Selected Problems
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## Update (March 24, 2026)
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This dataset was updated on March 24, 2026.
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Main changes:
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- added `eq1_id` and `eq2_id` to all released subsets
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- added the `hard3` subset
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- updated the README and metadata to reflect the current released subsets
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This dataset contains public training problem subsets selected from the Equational Theories Project raw implication dataset.
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This dataset is intended for Stage 1 of the Mathematics Distillation Challenge: Equational Theories competition.
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- `hard`: 200 selected problems co-curated by human mathematicians and AI, with 74 ground-truth `TRUE` labels and 126 ground-truth `FALSE` labels
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- `hard1`: a deduplicated version of the 200-problem `hard` subset, containing 69 unique problems total, with 24 ground-truth `TRUE` labels and 45 ground-truth `FALSE` labels
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- `hard2`: 200 selected problems co-curated by human mathematicians and AI, with 100 ground-truth `TRUE` labels and 100 ground-truth `FALSE` labels
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- `hard3`: 400 selected problems with 195 ground-truth `TRUE` labels and 205 ground-truth `FALSE` labels
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All subsets are public training problems and are exposed as the `train` split in this repository.
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Each record has the following fields:
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- `id`: stable identifier such as `normal_0001`, `hard_0001`, `hard1_0001`, `hard2_0001`, or `hard3_0001`
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- `index`: 1-based index within the subset
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- `difficulty`: `normal` or `hard`
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- `eq1_id`: 1-based equation identifier for `equation1` in the full 4694-law equation list
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- `eq2_id`: 1-based equation identifier for `equation2` in the full 4694-law equation list
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- `equation1`: Equation 1
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- `equation2`: Equation 2
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- `answer`: whether Equation 1 implies Equation 2 over all magmas
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- `derived_from`: parent subset name if the subset is derived from another subset
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- `notes`: optional explanatory notes
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Records in `hard1`, `hard2`, and `hard3` use subset-specific IDs and keep `difficulty: hard`.
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## Usage
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"hard2",
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split="train",
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)
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hard3 = load_dataset(
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"SAIRfoundation/equational-theories-selected-problems",
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"hard3",
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split="train",
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)
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```
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## Files
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- `data/hard.jsonl`
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- `data/hard1.jsonl`
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- `data/hard2.jsonl`
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- `data/hard3.jsonl`
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- `metadata/normal.json`
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- `metadata/hard.json`
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- `metadata/hard1.json`
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- `metadata/hard2.json`
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- `metadata/hard3.json`
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data/hard.jsonl
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{"id": "hard_0001", "index": 1, "difficulty": "hard", "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x * y = ((z * x) * w) * y", "answer": false}
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-
{"id": "hard_0002", "index": 2, "difficulty": "hard", "equation1": "x * (y * z) = (z * w) * w", "equation2": "x * (y * x) = (x * y) * z", "answer": false}
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{"id": "hard_0003", "index": 3, "difficulty": "hard", "equation1": "x = ((y * y) * z) * x", "equation2": "x = x * (((y * x) * x) * x)", "answer": true}
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-
{"id": "hard_0004", "index": 4, "difficulty": "hard", "equation1": "(x * y) * x = (x * z) * w", "equation2": "x * (y * y) = x * (z * y)", "answer": false}
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-
{"id": "hard_0005", "index": 5, "difficulty": "hard", "equation1": "x = ((y * z) * (z * x)) * y", "equation2": "x * x = (y * (y * y)) * y", "answer": false}
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-
{"id": "hard_0006", "index": 6, "difficulty": "hard", "equation1": "x * x = (x * y) * z", "equation2": "x * x = (y * z) * w", "answer": false}
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-
{"id": "hard_0007", "index": 7, "difficulty": "hard", "equation1": "x = (y * (y * (y * z))) * x", "equation2": "x * y = z * (w * (w * y))", "answer": true}
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-
{"id": "hard_0008", "index": 8, "difficulty": "hard", "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x = x * ((x * (x * x)) * x)", "answer": false}
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-
{"id": "hard_0009", "index": 9, "difficulty": "hard", "equation1": "x = ((x * x) * (y * z)) * y", "equation2": "x = ((x * (y * x)) * x) * y", "answer": false}
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-
{"id": "hard_0010", "index": 10, "difficulty": "hard", "equation1": "(x * x) * y = (y * y) * z", "equation2": "x * (y * y) = x * (z * z)", "answer": false}
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-
{"id": "hard_0011", "index": 11, "difficulty": "hard", "equation1": "x = (x * (y * z)) * (w * y)", "equation2": "x = (y * (z * w)) * (u * z)", "answer": false}
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-
{"id": "hard_0012", "index": 12, "difficulty": "hard", "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * x) = x * (y * y)", "answer": false}
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-
{"id": "hard_0013", "index": 13, "difficulty": "hard", "equation1": "x * y = ((z * y) * x) * x", "equation2": "x * y = y * (y * (y * y))", "answer": true}
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-
{"id": "hard_0014", "index": 14, "difficulty": "hard", "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = y * (z * (z * (x * y)))", "answer": false}
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-
{"id": "hard_0015", "index": 15, "difficulty": "hard", "equation1": "x * x = x * (y * (z * y))", "equation2": "x * (x * x) = x * (y * x)", "answer": false}
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-
{"id": "hard_0016", "index": 16, "difficulty": "hard", "equation1": "x = (x * y) * (x * (y * z))", "equation2": "x = (x * y) * (x * (z * y))", "answer": false}
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-
{"id": "hard_0017", "index": 17, "difficulty": "hard", "equation1": "x = y * (((x * y) * x) * y)", "equation2": "x = ((x * (y * z)) * z) * y", "answer": false}
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-
{"id": "hard_0018", "index": 18, "difficulty": "hard", "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
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-
{"id": "hard_0019", "index": 19, "difficulty": "hard", "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
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-
{"id": "hard_0020", "index": 20, "difficulty": "hard", "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
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-
{"id": "hard_0021", "index": 21, "difficulty": "hard", "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
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-
{"id": "hard_0022", "index": 22, "difficulty": "hard", "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
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-
{"id": "hard_0023", "index": 23, "difficulty": "hard", "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
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-
{"id": "hard_0024", "index": 24, "difficulty": "hard", "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
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{"id": "hard_0025", "index": 25, "difficulty": "hard", "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
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-
{"id": "hard_0026", "index": 26, "difficulty": "hard", "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
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{"id": "hard_0027", "index": 27, "difficulty": "hard", "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
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{"id": "hard_0028", "index": 28, "difficulty": "hard", "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
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{"id": "hard_0029", "index": 29, "difficulty": "hard", "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
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{"id": "hard_0030", "index": 30, "difficulty": "hard", "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
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{"id": "hard_0031", "index": 31, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
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{"id": "hard_0032", "index": 32, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
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-
{"id": "hard_0033", "index": 33, "difficulty": "hard", "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
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{"id": "hard_0034", "index": 34, "difficulty": "hard", "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
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{"id": "hard_0035", "index": 35, "difficulty": "hard", "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
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{"id": "hard_0036", "index": 36, "difficulty": "hard", "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
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{"id": "hard_0037", "index": 37, "difficulty": "hard", "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
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{"id": "hard_0038", "index": 38, "difficulty": "hard", "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
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{"id": "hard_0039", "index": 39, "difficulty": "hard", "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
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{"id": "hard_0040", "index": 40, "difficulty": "hard", "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
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{"id": "hard_0041", "index": 41, "difficulty": "hard", "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
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{"id": "hard_0042", "index": 42, "difficulty": "hard", "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
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-
{"id": "hard_0043", "index": 43, "difficulty": "hard", "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
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{"id": "hard_0044", "index": 44, "difficulty": "hard", "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
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-
{"id": "hard_0045", "index": 45, "difficulty": "hard", "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = (x * (y * z)) * (w * w)", "answer": false}
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{"id": "hard_0046", "index": 46, "difficulty": "hard", "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = y * (y * (y * y))", "answer": true}
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-
{"id": "hard_0047", "index": 47, "difficulty": "hard", "equation1": "x = (y * x) * (x * (z * z))", "equation2": "x = y * ((y * x) * (z * y))", "answer": false}
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-
{"id": "hard_0048", "index": 48, "difficulty": "hard", "equation1": "x = (y * (z * y)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": false}
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-
{"id": "hard_0049", "index": 49, "difficulty": "hard", "equation1": "x * (y * z) = (z * x) * y", "equation2": "x * (y * z) = (w * u) * y", "answer": false}
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-
{"id": "hard_0050", "index": 50, "difficulty": "hard", "equation1": "x = x * (((y * z) * w) * u)", "equation2": "x = ((x * x) * (x * y)) * y", "answer": true}
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-
{"id": "hard_0051", "index": 51, "difficulty": "hard", "equation1": "x * y = ((x * z) * w) * y", "equation2": "x * y = ((z * w) * x) * y", "answer": false}
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-
{"id": "hard_0052", "index": 52, "difficulty": "hard", "equation1": "x = (y * x) * (y * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
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-
{"id": "hard_0053", "index": 53, "difficulty": "hard", "equation1": "x * y = (x * z) * (y * w)", "equation2": "x * y = (x * y) * (z * x)", "answer": false}
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-
{"id": "hard_0054", "index": 54, "difficulty": "hard", "equation1": "x * y = ((z * w) * x) * u", "equation2": "x * (y * y) = (x * x) * x", "answer": true}
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-
{"id": "hard_0055", "index": 55, "difficulty": "hard", "equation1": "x = y * (((z * w) * x) * x)", "equation2": "x = y * (((z * x) * w) * w)", "answer": false}
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-
{"id": "hard_0056", "index": 56, "difficulty": "hard", "equation1": "x = (y * (y * z)) * (w * x)", "equation2": "x = y * (z * (w * (u * x)))", "answer": true}
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{"id": "hard_0057", "index": 57, "difficulty": "hard", "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x = y * (x * ((z * w) * x))", "answer": false}
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{"id": "hard_0058", "index": 58, "difficulty": "hard", "equation1": "x * (y * z) = (w * w) * z", "equation2": "x * (y * x) = (x * z) * x", "answer": false}
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{"id": "hard_0059", "index": 59, "difficulty": "hard", "equation1": "x = ((y * z) * z) * x", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
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{"id": "hard_0060", "index": 60, "difficulty": "hard", "equation1": "x = (((y * z) * x) * z) * x", "equation2": "x = y * (((x * y) * y) * x)", "answer": true}
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{"id": "hard_0061", "index": 61, "difficulty": "hard", "equation1": "x = x * (y * (z * (x * y)))", "equation2": "x = x * (((y * x) * z) * w)", "answer": true}
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{"id": "hard_0062", "index": 62, "difficulty": "hard", "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * (x * x))) * x", "answer": false}
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{"id": "hard_0063", "index": 63, "difficulty": "hard", "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * ((z * (w * u)) * x)", "answer": true}
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{"id": "hard_0064", "index": 64, "difficulty": "hard", "equation1": "x = x * ((y * z) * (z * z))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": true}
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{"id": "hard_0065", "index": 65, "difficulty": "hard", "equation1": "x = x * (y * (z * y))", "equation2": "x = (x * (x * (x * y))) * x", "answer": true}
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{"id": "hard_0066", "index": 66, "difficulty": "hard", "equation1": "x = ((y * z) * y) * (x * z)", "equation2": "x = (((y * x) * y) * y) * y", "answer": false}
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-
{"id": "hard_0067", "index": 67, "difficulty": "hard", "equation1": "x = (y * (y * x)) * (z * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
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-
{"id": "hard_0068", "index": 68, "difficulty": "hard", "equation1": "x * x = y * ((x * z) * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
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| 69 |
-
{"id": "hard_0069", "index": 69, "difficulty": "hard", "equation1": "x = ((y * y) * z) * x", "equation2": "x = y * (y * (z * (w * x)))", "answer": true}
|
| 70 |
-
{"id": "hard_0070", "index": 70, "difficulty": "hard", "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 71 |
-
{"id": "hard_0071", "index": 71, "difficulty": "hard", "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 72 |
-
{"id": "hard_0072", "index": 72, "difficulty": "hard", "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 73 |
-
{"id": "hard_0073", "index": 73, "difficulty": "hard", "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 74 |
-
{"id": "hard_0074", "index": 74, "difficulty": "hard", "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 75 |
-
{"id": "hard_0075", "index": 75, "difficulty": "hard", "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 76 |
-
{"id": "hard_0076", "index": 76, "difficulty": "hard", "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 77 |
-
{"id": "hard_0077", "index": 77, "difficulty": "hard", "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 78 |
-
{"id": "hard_0078", "index": 78, "difficulty": "hard", "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 79 |
-
{"id": "hard_0079", "index": 79, "difficulty": "hard", "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 80 |
-
{"id": "hard_0080", "index": 80, "difficulty": "hard", "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 81 |
-
{"id": "hard_0081", "index": 81, "difficulty": "hard", "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 82 |
-
{"id": "hard_0082", "index": 82, "difficulty": "hard", "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 83 |
-
{"id": "hard_0083", "index": 83, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 84 |
-
{"id": "hard_0084", "index": 84, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 85 |
-
{"id": "hard_0085", "index": 85, "difficulty": "hard", "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 86 |
-
{"id": "hard_0086", "index": 86, "difficulty": "hard", "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 87 |
-
{"id": "hard_0087", "index": 87, "difficulty": "hard", "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 88 |
-
{"id": "hard_0088", "index": 88, "difficulty": "hard", "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 89 |
-
{"id": "hard_0089", "index": 89, "difficulty": "hard", "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 90 |
-
{"id": "hard_0090", "index": 90, "difficulty": "hard", "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 91 |
-
{"id": "hard_0091", "index": 91, "difficulty": "hard", "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 92 |
-
{"id": "hard_0092", "index": 92, "difficulty": "hard", "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 93 |
-
{"id": "hard_0093", "index": 93, "difficulty": "hard", "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 94 |
-
{"id": "hard_0094", "index": 94, "difficulty": "hard", "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 95 |
-
{"id": "hard_0095", "index": 95, "difficulty": "hard", "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 96 |
-
{"id": "hard_0096", "index": 96, "difficulty": "hard", "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
| 97 |
-
{"id": "hard_0097", "index": 97, "difficulty": "hard", "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = (x * (y * z)) * (w * w)", "answer": false}
|
| 98 |
-
{"id": "hard_0098", "index": 98, "difficulty": "hard", "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = y * (y * (y * y))", "answer": true}
|
| 99 |
-
{"id": "hard_0099", "index": 99, "difficulty": "hard", "equation1": "x = (y * x) * (x * (z * z))", "equation2": "x = y * ((y * x) * (z * y))", "answer": false}
|
| 100 |
-
{"id": "hard_0100", "index": 100, "difficulty": "hard", "equation1": "x = (y * (z * y)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": false}
|
| 101 |
-
{"id": "hard_0101", "index": 101, "difficulty": "hard", "equation1": "x * (y * z) = (z * x) * y", "equation2": "x * (y * z) = (w * u) * y", "answer": false}
|
| 102 |
-
{"id": "hard_0102", "index": 102, "difficulty": "hard", "equation1": "x = x * (((y * z) * w) * u)", "equation2": "x = ((x * x) * (x * y)) * y", "answer": true}
|
| 103 |
-
{"id": "hard_0103", "index": 103, "difficulty": "hard", "equation1": "x * y = ((x * z) * w) * y", "equation2": "x * y = ((z * w) * x) * y", "answer": false}
|
| 104 |
-
{"id": "hard_0104", "index": 104, "difficulty": "hard", "equation1": "x = (y * x) * (y * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
|
| 105 |
-
{"id": "hard_0105", "index": 105, "difficulty": "hard", "equation1": "x * y = (x * z) * (y * w)", "equation2": "x * y = (x * y) * (z * x)", "answer": false}
|
| 106 |
-
{"id": "hard_0106", "index": 106, "difficulty": "hard", "equation1": "x * y = ((z * w) * x) * u", "equation2": "x * (y * y) = (x * x) * x", "answer": true}
|
| 107 |
-
{"id": "hard_0107", "index": 107, "difficulty": "hard", "equation1": "x = y * (((z * w) * x) * x)", "equation2": "x = y * (((z * x) * w) * w)", "answer": false}
|
| 108 |
-
{"id": "hard_0108", "index": 108, "difficulty": "hard", "equation1": "x = (y * (y * z)) * (w * x)", "equation2": "x = y * (z * (w * (u * x)))", "answer": true}
|
| 109 |
-
{"id": "hard_0109", "index": 109, "difficulty": "hard", "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x = y * (x * ((z * w) * x))", "answer": false}
|
| 110 |
-
{"id": "hard_0110", "index": 110, "difficulty": "hard", "equation1": "x * (y * z) = (w * w) * z", "equation2": "x * (y * x) = (x * z) * x", "answer": false}
|
| 111 |
-
{"id": "hard_0111", "index": 111, "difficulty": "hard", "equation1": "x = ((y * z) * z) * x", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 112 |
-
{"id": "hard_0112", "index": 112, "difficulty": "hard", "equation1": "x = (((y * z) * x) * z) * x", "equation2": "x = y * (((x * y) * y) * x)", "answer": true}
|
| 113 |
-
{"id": "hard_0113", "index": 113, "difficulty": "hard", "equation1": "x = x * (y * (z * (x * y)))", "equation2": "x = x * (((y * x) * z) * w)", "answer": true}
|
| 114 |
-
{"id": "hard_0114", "index": 114, "difficulty": "hard", "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * (x * x))) * x", "answer": false}
|
| 115 |
-
{"id": "hard_0115", "index": 115, "difficulty": "hard", "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * ((z * (w * u)) * x)", "answer": true}
|
| 116 |
-
{"id": "hard_0116", "index": 116, "difficulty": "hard", "equation1": "x = x * ((y * z) * (z * z))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": true}
|
| 117 |
-
{"id": "hard_0117", "index": 117, "difficulty": "hard", "equation1": "x = x * (y * (z * y))", "equation2": "x = (x * (x * (x * y))) * x", "answer": true}
|
| 118 |
-
{"id": "hard_0118", "index": 118, "difficulty": "hard", "equation1": "x = ((y * z) * y) * (x * z)", "equation2": "x = (((y * x) * y) * y) * y", "answer": false}
|
| 119 |
-
{"id": "hard_0119", "index": 119, "difficulty": "hard", "equation1": "x = (y * (y * x)) * (z * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
|
| 120 |
-
{"id": "hard_0120", "index": 120, "difficulty": "hard", "equation1": "x * x = y * ((x * z) * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 121 |
-
{"id": "hard_0121", "index": 121, "difficulty": "hard", "equation1": "x = ((y * y) * z) * x", "equation2": "x = y * (y * (z * (w * x)))", "answer": true}
|
| 122 |
-
{"id": "hard_0122", "index": 122, "difficulty": "hard", "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 123 |
-
{"id": "hard_0123", "index": 123, "difficulty": "hard", "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 124 |
-
{"id": "hard_0124", "index": 124, "difficulty": "hard", "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 125 |
-
{"id": "hard_0125", "index": 125, "difficulty": "hard", "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 126 |
-
{"id": "hard_0126", "index": 126, "difficulty": "hard", "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 127 |
-
{"id": "hard_0127", "index": 127, "difficulty": "hard", "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 128 |
-
{"id": "hard_0128", "index": 128, "difficulty": "hard", "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 129 |
-
{"id": "hard_0129", "index": 129, "difficulty": "hard", "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 130 |
-
{"id": "hard_0130", "index": 130, "difficulty": "hard", "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 131 |
-
{"id": "hard_0131", "index": 131, "difficulty": "hard", "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 132 |
-
{"id": "hard_0132", "index": 132, "difficulty": "hard", "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 133 |
-
{"id": "hard_0133", "index": 133, "difficulty": "hard", "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 134 |
-
{"id": "hard_0134", "index": 134, "difficulty": "hard", "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 135 |
-
{"id": "hard_0135", "index": 135, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 136 |
-
{"id": "hard_0136", "index": 136, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 137 |
-
{"id": "hard_0137", "index": 137, "difficulty": "hard", "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 138 |
-
{"id": "hard_0138", "index": 138, "difficulty": "hard", "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 139 |
-
{"id": "hard_0139", "index": 139, "difficulty": "hard", "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 140 |
-
{"id": "hard_0140", "index": 140, "difficulty": "hard", "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 141 |
-
{"id": "hard_0141", "index": 141, "difficulty": "hard", "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 142 |
-
{"id": "hard_0142", "index": 142, "difficulty": "hard", "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 143 |
-
{"id": "hard_0143", "index": 143, "difficulty": "hard", "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 144 |
-
{"id": "hard_0144", "index": 144, "difficulty": "hard", "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 145 |
-
{"id": "hard_0145", "index": 145, "difficulty": "hard", "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 146 |
-
{"id": "hard_0146", "index": 146, "difficulty": "hard", "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 147 |
-
{"id": "hard_0147", "index": 147, "difficulty": "hard", "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 148 |
-
{"id": "hard_0148", "index": 148, "difficulty": "hard", "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
| 149 |
-
{"id": "hard_0149", "index": 149, "difficulty": "hard", "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = (x * (y * z)) * (w * w)", "answer": false}
|
| 150 |
-
{"id": "hard_0150", "index": 150, "difficulty": "hard", "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = y * (y * (y * y))", "answer": true}
|
| 151 |
-
{"id": "hard_0151", "index": 151, "difficulty": "hard", "equation1": "x = (y * x) * (x * (z * z))", "equation2": "x = y * ((y * x) * (z * y))", "answer": false}
|
| 152 |
-
{"id": "hard_0152", "index": 152, "difficulty": "hard", "equation1": "x = (y * (z * y)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": false}
|
| 153 |
-
{"id": "hard_0153", "index": 153, "difficulty": "hard", "equation1": "x * (y * z) = (z * x) * y", "equation2": "x * (y * z) = (w * u) * y", "answer": false}
|
| 154 |
-
{"id": "hard_0154", "index": 154, "difficulty": "hard", "equation1": "x = x * (((y * z) * w) * u)", "equation2": "x = ((x * x) * (x * y)) * y", "answer": true}
|
| 155 |
-
{"id": "hard_0155", "index": 155, "difficulty": "hard", "equation1": "x * y = ((x * z) * w) * y", "equation2": "x * y = ((z * w) * x) * y", "answer": false}
|
| 156 |
-
{"id": "hard_0156", "index": 156, "difficulty": "hard", "equation1": "x = (y * x) * (y * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
|
| 157 |
-
{"id": "hard_0157", "index": 157, "difficulty": "hard", "equation1": "x * y = (x * z) * (y * w)", "equation2": "x * y = (x * y) * (z * x)", "answer": false}
|
| 158 |
-
{"id": "hard_0158", "index": 158, "difficulty": "hard", "equation1": "x * y = ((z * w) * x) * u", "equation2": "x * (y * y) = (x * x) * x", "answer": true}
|
| 159 |
-
{"id": "hard_0159", "index": 159, "difficulty": "hard", "equation1": "x = y * (((z * w) * x) * x)", "equation2": "x = y * (((z * x) * w) * w)", "answer": false}
|
| 160 |
-
{"id": "hard_0160", "index": 160, "difficulty": "hard", "equation1": "x = (y * (y * z)) * (w * x)", "equation2": "x = y * (z * (w * (u * x)))", "answer": true}
|
| 161 |
-
{"id": "hard_0161", "index": 161, "difficulty": "hard", "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x = y * (x * ((z * w) * x))", "answer": false}
|
| 162 |
-
{"id": "hard_0162", "index": 162, "difficulty": "hard", "equation1": "x * (y * z) = (w * w) * z", "equation2": "x * (y * x) = (x * z) * x", "answer": false}
|
| 163 |
-
{"id": "hard_0163", "index": 163, "difficulty": "hard", "equation1": "x = ((y * z) * z) * x", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 164 |
-
{"id": "hard_0164", "index": 164, "difficulty": "hard", "equation1": "x = (((y * z) * x) * z) * x", "equation2": "x = y * (((x * y) * y) * x)", "answer": true}
|
| 165 |
-
{"id": "hard_0165", "index": 165, "difficulty": "hard", "equation1": "x = x * (y * (z * (x * y)))", "equation2": "x = x * (((y * x) * z) * w)", "answer": true}
|
| 166 |
-
{"id": "hard_0166", "index": 166, "difficulty": "hard", "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * (x * x))) * x", "answer": false}
|
| 167 |
-
{"id": "hard_0167", "index": 167, "difficulty": "hard", "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * ((z * (w * u)) * x)", "answer": true}
|
| 168 |
-
{"id": "hard_0168", "index": 168, "difficulty": "hard", "equation1": "x = x * ((y * z) * (z * z))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": true}
|
| 169 |
-
{"id": "hard_0169", "index": 169, "difficulty": "hard", "equation1": "x = x * (y * (z * y))", "equation2": "x = (x * (x * (x * y))) * x", "answer": true}
|
| 170 |
-
{"id": "hard_0170", "index": 170, "difficulty": "hard", "equation1": "x = ((y * z) * y) * (x * z)", "equation2": "x = (((y * x) * y) * y) * y", "answer": false}
|
| 171 |
-
{"id": "hard_0171", "index": 171, "difficulty": "hard", "equation1": "x = (y * (y * x)) * (z * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
|
| 172 |
-
{"id": "hard_0172", "index": 172, "difficulty": "hard", "equation1": "x * x = y * ((x * z) * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 173 |
-
{"id": "hard_0173", "index": 173, "difficulty": "hard", "equation1": "x = ((y * y) * z) * x", "equation2": "x = y * (y * (z * (w * x)))", "answer": true}
|
| 174 |
-
{"id": "hard_0174", "index": 174, "difficulty": "hard", "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 175 |
-
{"id": "hard_0175", "index": 175, "difficulty": "hard", "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 176 |
-
{"id": "hard_0176", "index": 176, "difficulty": "hard", "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 177 |
-
{"id": "hard_0177", "index": 177, "difficulty": "hard", "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 178 |
-
{"id": "hard_0178", "index": 178, "difficulty": "hard", "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 179 |
-
{"id": "hard_0179", "index": 179, "difficulty": "hard", "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 180 |
-
{"id": "hard_0180", "index": 180, "difficulty": "hard", "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 181 |
-
{"id": "hard_0181", "index": 181, "difficulty": "hard", "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 182 |
-
{"id": "hard_0182", "index": 182, "difficulty": "hard", "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 183 |
-
{"id": "hard_0183", "index": 183, "difficulty": "hard", "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 184 |
-
{"id": "hard_0184", "index": 184, "difficulty": "hard", "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 185 |
-
{"id": "hard_0185", "index": 185, "difficulty": "hard", "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 186 |
-
{"id": "hard_0186", "index": 186, "difficulty": "hard", "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 187 |
-
{"id": "hard_0187", "index": 187, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 188 |
-
{"id": "hard_0188", "index": 188, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 189 |
-
{"id": "hard_0189", "index": 189, "difficulty": "hard", "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 190 |
-
{"id": "hard_0190", "index": 190, "difficulty": "hard", "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 191 |
-
{"id": "hard_0191", "index": 191, "difficulty": "hard", "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 192 |
-
{"id": "hard_0192", "index": 192, "difficulty": "hard", "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 193 |
-
{"id": "hard_0193", "index": 193, "difficulty": "hard", "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 194 |
-
{"id": "hard_0194", "index": 194, "difficulty": "hard", "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 195 |
-
{"id": "hard_0195", "index": 195, "difficulty": "hard", "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 196 |
-
{"id": "hard_0196", "index": 196, "difficulty": "hard", "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 197 |
-
{"id": "hard_0197", "index": 197, "difficulty": "hard", "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 198 |
-
{"id": "hard_0198", "index": 198, "difficulty": "hard", "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 199 |
-
{"id": "hard_0199", "index": 199, "difficulty": "hard", "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 200 |
-
{"id": "hard_0200", "index": 200, "difficulty": "hard", "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
|
|
|
| 1 |
+
{"id": "hard_0001", "index": 1, "difficulty": "hard", "eq1_id": 706, "eq2_id": 4204, "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x * y = ((z * x) * w) * y", "answer": false}
|
| 2 |
+
{"id": "hard_0002", "index": 2, "difficulty": "hard", "eq1_id": 4555, "eq2_id": 4437, "equation1": "x * (y * z) = (z * w) * w", "equation2": "x * (y * x) = (x * y) * z", "answer": false}
|
| 3 |
+
{"id": "hard_0003", "index": 3, "difficulty": "hard", "eq1_id": 286, "eq2_id": 1238, "equation1": "x = ((y * y) * z) * x", "equation2": "x = x * (((y * x) * x) * x)", "answer": true}
|
| 4 |
+
{"id": "hard_0004", "index": 4, "difficulty": "hard", "eq1_id": 4634, "eq2_id": 4340, "equation1": "(x * y) * x = (x * z) * w", "equation2": "x * (y * y) = x * (z * y)", "answer": false}
|
| 5 |
+
{"id": "hard_0005", "index": 5, "difficulty": "hard", "eq1_id": 2805, "eq2_id": 3891, "equation1": "x = ((y * z) * (z * x)) * y", "equation2": "x * x = (y * (y * y)) * y", "answer": false}
|
| 6 |
+
{"id": "hard_0006", "index": 6, "difficulty": "hard", "eq1_id": 363, "eq2_id": 373, "equation1": "x * x = (x * y) * z", "equation2": "x * x = (y * z) * w", "answer": false}
|
| 7 |
+
{"id": "hard_0007", "index": 7, "difficulty": "hard", "eq1_id": 2343, "eq2_id": 3446, "equation1": "x = (y * (y * (y * z))) * x", "equation2": "x * y = z * (w * (w * y))", "answer": true}
|
| 8 |
+
{"id": "hard_0008", "index": 8, "difficulty": "hard", "eq1_id": 646, "eq2_id": 1020, "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x = x * ((x * (x * x)) * x)", "answer": false}
|
| 9 |
+
{"id": "hard_0009", "index": 9, "difficulty": "hard", "eq1_id": 2656, "eq2_id": 2863, "equation1": "x = ((x * x) * (y * z)) * y", "equation2": "x = ((x * (y * x)) * x) * y", "answer": false}
|
| 10 |
+
{"id": "hard_0010", "index": 10, "difficulty": "hard", "eq1_id": 4609, "eq2_id": 4341, "equation1": "(x * x) * y = (y * y) * z", "equation2": "x * (y * y) = x * (z * z)", "answer": false}
|
| 11 |
+
{"id": "hard_0011", "index": 11, "difficulty": "hard", "eq1_id": 1880, "eq2_id": 2031, "equation1": "x = (x * (y * z)) * (w * y)", "equation2": "x = (y * (z * w)) * (u * z)", "answer": false}
|
| 12 |
+
{"id": "hard_0012", "index": 12, "difficulty": "hard", "eq1_id": 4653, "eq2_id": 4270, "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * x) = x * (y * y)", "answer": false}
|
| 13 |
+
{"id": "hard_0013", "index": 13, "difficulty": "hard", "eq1_id": 4208, "eq2_id": 3356, "equation1": "x * y = ((z * y) * x) * x", "equation2": "x * y = y * (y * (y * y))", "answer": true}
|
| 14 |
+
{"id": "hard_0014", "index": 14, "difficulty": "hard", "eq1_id": 1480, "eq2_id": 572, "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = y * (z * (z * (x * y)))", "answer": false}
|
| 15 |
+
{"id": "hard_0015", "index": 15, "difficulty": "hard", "eq1_id": 3265, "eq2_id": 4269, "equation1": "x * x = x * (y * (z * y))", "equation2": "x * (x * x) = x * (y * x)", "answer": false}
|
| 16 |
+
{"id": "hard_0016", "index": 16, "difficulty": "hard", "eq1_id": 1446, "eq2_id": 1448, "equation1": "x = (x * y) * (x * (y * z))", "equation2": "x = (x * y) * (x * (z * y))", "answer": false}
|
| 17 |
+
{"id": "hard_0017", "index": 17, "difficulty": "hard", "eq1_id": 1286, "eq2_id": 2891, "equation1": "x = y * (((x * y) * x) * y)", "equation2": "x = ((x * (y * z)) * z) * y", "answer": false}
|
| 18 |
+
{"id": "hard_0018", "index": 18, "difficulty": "hard", "eq1_id": 2105, "eq2_id": 1229, "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 19 |
+
{"id": "hard_0019", "index": 19, "difficulty": "hard", "eq1_id": 3926, "eq2_id": 3920, "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 20 |
+
{"id": "hard_0020", "index": 20, "difficulty": "hard", "eq1_id": 4508, "eq2_id": 4527, "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 21 |
+
{"id": "hard_0021", "index": 21, "difficulty": "hard", "eq1_id": 907, "eq2_id": 221, "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 22 |
+
{"id": "hard_0022", "index": 22, "difficulty": "hard", "eq1_id": 3961, "eq2_id": 3722, "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 23 |
+
{"id": "hard_0023", "index": 23, "difficulty": "hard", "eq1_id": 164, "eq2_id": 3470, "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 24 |
+
{"id": "hard_0024", "index": 24, "difficulty": "hard", "eq1_id": 706, "eq2_id": 860, "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 25 |
+
{"id": "hard_0025", "index": 25, "difficulty": "hard", "eq1_id": 3008, "eq2_id": 1131, "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 26 |
+
{"id": "hard_0026", "index": 26, "difficulty": "hard", "eq1_id": 2890, "eq2_id": 3261, "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 27 |
+
{"id": "hard_0027", "index": 27, "difficulty": "hard", "eq1_id": 54, "eq2_id": 2695, "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 28 |
+
{"id": "hard_0028", "index": 28, "difficulty": "hard", "eq1_id": 3583, "eq2_id": 4406, "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 29 |
+
{"id": "hard_0029", "index": 29, "difficulty": "hard", "eq1_id": 1738, "eq2_id": 3972, "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 30 |
+
{"id": "hard_0030", "index": 30, "difficulty": "hard", "eq1_id": 2301, "eq2_id": 4303, "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 31 |
+
{"id": "hard_0031", "index": 31, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 900, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 32 |
+
{"id": "hard_0032", "index": 32, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 404, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 33 |
+
{"id": "hard_0033", "index": 33, "difficulty": "hard", "eq1_id": 2994, "eq2_id": 2623, "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 34 |
+
{"id": "hard_0034", "index": 34, "difficulty": "hard", "eq1_id": 386, "eq2_id": 3639, "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 35 |
+
{"id": "hard_0035", "index": 35, "difficulty": "hard", "eq1_id": 868, "eq2_id": 2243, "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 36 |
+
{"id": "hard_0036", "index": 36, "difficulty": "hard", "eq1_id": 3290, "eq2_id": 3264, "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 37 |
+
{"id": "hard_0037", "index": 37, "difficulty": "hard", "eq1_id": 1336, "eq2_id": 419, "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 38 |
+
{"id": "hard_0038", "index": 38, "difficulty": "hard", "eq1_id": 3919, "eq2_id": 3330, "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 39 |
+
{"id": "hard_0039", "index": 39, "difficulty": "hard", "eq1_id": 830, "eq2_id": 1229, "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 40 |
+
{"id": "hard_0040", "index": 40, "difficulty": "hard", "eq1_id": 1070, "eq2_id": 3950, "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 41 |
+
{"id": "hard_0041", "index": 41, "difficulty": "hard", "eq1_id": 3118, "eq2_id": 3441, "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 42 |
+
{"id": "hard_0042", "index": 42, "difficulty": "hard", "eq1_id": 168, "eq2_id": 431, "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 43 |
+
{"id": "hard_0043", "index": 43, "difficulty": "hard", "eq1_id": 3277, "eq2_id": 3473, "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 44 |
+
{"id": "hard_0044", "index": 44, "difficulty": "hard", "eq1_id": 234, "eq2_id": 3065, "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
| 45 |
+
{"id": "hard_0045", "index": 45, "difficulty": "hard", "eq1_id": 1480, "eq2_id": 1882, "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = (x * (y * z)) * (w * w)", "answer": false}
|
| 46 |
+
{"id": "hard_0046", "index": 46, "difficulty": "hard", "eq1_id": 3550, "eq2_id": 3282, "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = y * (y * (y * y))", "answer": true}
|
| 47 |
+
{"id": "hard_0047", "index": 47, "difficulty": "hard", "eq1_id": 1486, "eq2_id": 913, "equation1": "x = (y * x) * (x * (z * z))", "equation2": "x = y * ((y * x) * (z * y))", "answer": false}
|
| 48 |
+
{"id": "hard_0048", "index": 48, "difficulty": "hard", "eq1_id": 242, "eq2_id": 3197, "equation1": "x = (y * (z * y)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": false}
|
| 49 |
+
{"id": "hard_0049", "index": 49, "difficulty": "hard", "eq1_id": 4541, "eq2_id": 4578, "equation1": "x * (y * z) = (z * x) * y", "equation2": "x * (y * z) = (w * u) * y", "answer": false}
|
| 50 |
+
{"id": "hard_0050", "index": 50, "difficulty": "hard", "eq1_id": 1274, "eq2_id": 2647, "equation1": "x = x * (((y * z) * w) * u)", "equation2": "x = ((x * x) * (x * y)) * y", "answer": true}
|
| 51 |
+
{"id": "hard_0051", "index": 51, "difficulty": "hard", "eq1_id": 4150, "eq2_id": 4243, "equation1": "x * y = ((x * z) * w) * y", "equation2": "x * y = ((z * w) * x) * y", "answer": false}
|
| 52 |
+
{"id": "hard_0052", "index": 52, "difficulty": "hard", "eq1_id": 169, "eq2_id": 2056, "equation1": "x = (y * x) * (y * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
|
| 53 |
+
{"id": "hard_0053", "index": 53, "difficulty": "hard", "eq1_id": 3738, "eq2_id": 3727, "equation1": "x * y = (x * z) * (y * w)", "equation2": "x * y = (x * y) * (z * x)", "answer": false}
|
| 54 |
+
{"id": "hard_0054", "index": 54, "difficulty": "hard", "eq1_id": 4246, "eq2_id": 4469, "equation1": "x * y = ((z * w) * x) * u", "equation2": "x * (y * y) = (x * x) * x", "answer": true}
|
| 55 |
+
{"id": "hard_0055", "index": 55, "difficulty": "hard", "eq1_id": 1400, "eq2_id": 1364, "equation1": "x = y * (((z * w) * x) * x)", "equation2": "x = y * (((z * x) * w) * w)", "answer": false}
|
| 56 |
+
{"id": "hard_0056", "index": 56, "difficulty": "hard", "eq1_id": 1953, "eq2_id": 608, "equation1": "x = (y * (y * z)) * (w * x)", "equation2": "x = y * (z * (w * (u * x)))", "answer": true}
|
| 57 |
+
{"id": "hard_0057", "index": 57, "difficulty": "hard", "eq1_id": 964, "eq2_id": 698, "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x = y * (x * ((z * w) * x))", "answer": false}
|
| 58 |
+
{"id": "hard_0058", "index": 58, "difficulty": "hard", "eq1_id": 4574, "eq2_id": 4438, "equation1": "x * (y * z) = (w * w) * z", "equation2": "x * (y * x) = (x * z) * x", "answer": false}
|
| 59 |
+
{"id": "hard_0059", "index": 59, "difficulty": "hard", "eq1_id": 298, "eq2_id": 1045, "equation1": "x = ((y * z) * z) * x", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 60 |
+
{"id": "hard_0060", "index": 60, "difficulty": "hard", "eq1_id": 3184, "eq2_id": 1288, "equation1": "x = (((y * z) * x) * z) * x", "equation2": "x = y * (((x * y) * y) * x)", "answer": true}
|
| 61 |
+
{"id": "hard_0061", "index": 61, "difficulty": "hard", "eq1_id": 447, "eq2_id": 1247, "equation1": "x = x * (y * (z * (x * y)))", "equation2": "x = x * (((y * x) * z) * w)", "answer": true}
|
| 62 |
+
{"id": "hard_0062", "index": 62, "difficulty": "hard", "eq1_id": 2116, "eq2_id": 2327, "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * (x * x))) * x", "answer": false}
|
| 63 |
+
{"id": "hard_0063", "index": 63, "difficulty": "hard", "eq1_id": 302, "eq2_id": 1217, "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * ((z * (w * u)) * x)", "answer": true}
|
| 64 |
+
{"id": "hard_0064", "index": 64, "difficulty": "hard", "eq1_id": 862, "eq2_id": 2466, "equation1": "x = x * ((y * z) * (z * z))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": true}
|
| 65 |
+
{"id": "hard_0065", "index": 65, "difficulty": "hard", "eq1_id": 59, "eq2_id": 2240, "equation1": "x = x * (y * (z * y))", "equation2": "x = (x * (x * (x * y))) * x", "answer": true}
|
| 66 |
+
{"id": "hard_0066", "index": 66, "difficulty": "hard", "eq1_id": 2180, "eq2_id": 3116, "equation1": "x = ((y * z) * y) * (x * z)", "equation2": "x = (((y * x) * y) * y) * y", "answer": false}
|
| 67 |
+
{"id": "hard_0067", "index": 67, "difficulty": "hard", "eq1_id": 1927, "eq2_id": 3409, "equation1": "x = (y * (y * x)) * (z * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
|
| 68 |
+
{"id": "hard_0068", "index": 68, "difficulty": "hard", "eq1_id": 3478, "eq2_id": 4316, "equation1": "x * x = y * ((x * z) * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 69 |
+
{"id": "hard_0069", "index": 69, "difficulty": "hard", "eq1_id": 286, "eq2_id": 532, "equation1": "x = ((y * y) * z) * x", "equation2": "x = y * (y * (z * (w * x)))", "answer": true}
|
| 70 |
+
{"id": "hard_0070", "index": 70, "difficulty": "hard", "eq1_id": 2105, "eq2_id": 1229, "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 71 |
+
{"id": "hard_0071", "index": 71, "difficulty": "hard", "eq1_id": 3926, "eq2_id": 3920, "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 72 |
+
{"id": "hard_0072", "index": 72, "difficulty": "hard", "eq1_id": 4508, "eq2_id": 4527, "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 73 |
+
{"id": "hard_0073", "index": 73, "difficulty": "hard", "eq1_id": 907, "eq2_id": 221, "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 74 |
+
{"id": "hard_0074", "index": 74, "difficulty": "hard", "eq1_id": 3961, "eq2_id": 3722, "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 75 |
+
{"id": "hard_0075", "index": 75, "difficulty": "hard", "eq1_id": 164, "eq2_id": 3470, "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 76 |
+
{"id": "hard_0076", "index": 76, "difficulty": "hard", "eq1_id": 706, "eq2_id": 860, "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 77 |
+
{"id": "hard_0077", "index": 77, "difficulty": "hard", "eq1_id": 3008, "eq2_id": 1131, "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 78 |
+
{"id": "hard_0078", "index": 78, "difficulty": "hard", "eq1_id": 2890, "eq2_id": 3261, "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 79 |
+
{"id": "hard_0079", "index": 79, "difficulty": "hard", "eq1_id": 54, "eq2_id": 2695, "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 80 |
+
{"id": "hard_0080", "index": 80, "difficulty": "hard", "eq1_id": 3583, "eq2_id": 4406, "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 81 |
+
{"id": "hard_0081", "index": 81, "difficulty": "hard", "eq1_id": 1738, "eq2_id": 3972, "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 82 |
+
{"id": "hard_0082", "index": 82, "difficulty": "hard", "eq1_id": 2301, "eq2_id": 4303, "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 83 |
+
{"id": "hard_0083", "index": 83, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 900, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 84 |
+
{"id": "hard_0084", "index": 84, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 404, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 85 |
+
{"id": "hard_0085", "index": 85, "difficulty": "hard", "eq1_id": 2994, "eq2_id": 2623, "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 86 |
+
{"id": "hard_0086", "index": 86, "difficulty": "hard", "eq1_id": 386, "eq2_id": 3639, "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 87 |
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{"id": "hard_0087", "index": 87, "difficulty": "hard", "eq1_id": 868, "eq2_id": 2243, "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 88 |
+
{"id": "hard_0088", "index": 88, "difficulty": "hard", "eq1_id": 3290, "eq2_id": 3264, "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 89 |
+
{"id": "hard_0089", "index": 89, "difficulty": "hard", "eq1_id": 1336, "eq2_id": 419, "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 90 |
+
{"id": "hard_0090", "index": 90, "difficulty": "hard", "eq1_id": 3919, "eq2_id": 3330, "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 91 |
+
{"id": "hard_0091", "index": 91, "difficulty": "hard", "eq1_id": 830, "eq2_id": 1229, "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 92 |
+
{"id": "hard_0092", "index": 92, "difficulty": "hard", "eq1_id": 1070, "eq2_id": 3950, "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 93 |
+
{"id": "hard_0093", "index": 93, "difficulty": "hard", "eq1_id": 3118, "eq2_id": 3441, "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 94 |
+
{"id": "hard_0094", "index": 94, "difficulty": "hard", "eq1_id": 168, "eq2_id": 431, "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 95 |
+
{"id": "hard_0095", "index": 95, "difficulty": "hard", "eq1_id": 3277, "eq2_id": 3473, "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 96 |
+
{"id": "hard_0096", "index": 96, "difficulty": "hard", "eq1_id": 234, "eq2_id": 3065, "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
| 97 |
+
{"id": "hard_0097", "index": 97, "difficulty": "hard", "eq1_id": 1480, "eq2_id": 1882, "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = (x * (y * z)) * (w * w)", "answer": false}
|
| 98 |
+
{"id": "hard_0098", "index": 98, "difficulty": "hard", "eq1_id": 3550, "eq2_id": 3282, "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = y * (y * (y * y))", "answer": true}
|
| 99 |
+
{"id": "hard_0099", "index": 99, "difficulty": "hard", "eq1_id": 1486, "eq2_id": 913, "equation1": "x = (y * x) * (x * (z * z))", "equation2": "x = y * ((y * x) * (z * y))", "answer": false}
|
| 100 |
+
{"id": "hard_0100", "index": 100, "difficulty": "hard", "eq1_id": 242, "eq2_id": 3197, "equation1": "x = (y * (z * y)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": false}
|
| 101 |
+
{"id": "hard_0101", "index": 101, "difficulty": "hard", "eq1_id": 4541, "eq2_id": 4578, "equation1": "x * (y * z) = (z * x) * y", "equation2": "x * (y * z) = (w * u) * y", "answer": false}
|
| 102 |
+
{"id": "hard_0102", "index": 102, "difficulty": "hard", "eq1_id": 1274, "eq2_id": 2647, "equation1": "x = x * (((y * z) * w) * u)", "equation2": "x = ((x * x) * (x * y)) * y", "answer": true}
|
| 103 |
+
{"id": "hard_0103", "index": 103, "difficulty": "hard", "eq1_id": 4150, "eq2_id": 4243, "equation1": "x * y = ((x * z) * w) * y", "equation2": "x * y = ((z * w) * x) * y", "answer": false}
|
| 104 |
+
{"id": "hard_0104", "index": 104, "difficulty": "hard", "eq1_id": 169, "eq2_id": 2056, "equation1": "x = (y * x) * (y * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
|
| 105 |
+
{"id": "hard_0105", "index": 105, "difficulty": "hard", "eq1_id": 3738, "eq2_id": 3727, "equation1": "x * y = (x * z) * (y * w)", "equation2": "x * y = (x * y) * (z * x)", "answer": false}
|
| 106 |
+
{"id": "hard_0106", "index": 106, "difficulty": "hard", "eq1_id": 4246, "eq2_id": 4469, "equation1": "x * y = ((z * w) * x) * u", "equation2": "x * (y * y) = (x * x) * x", "answer": true}
|
| 107 |
+
{"id": "hard_0107", "index": 107, "difficulty": "hard", "eq1_id": 1400, "eq2_id": 1364, "equation1": "x = y * (((z * w) * x) * x)", "equation2": "x = y * (((z * x) * w) * w)", "answer": false}
|
| 108 |
+
{"id": "hard_0108", "index": 108, "difficulty": "hard", "eq1_id": 1953, "eq2_id": 608, "equation1": "x = (y * (y * z)) * (w * x)", "equation2": "x = y * (z * (w * (u * x)))", "answer": true}
|
| 109 |
+
{"id": "hard_0109", "index": 109, "difficulty": "hard", "eq1_id": 964, "eq2_id": 698, "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x = y * (x * ((z * w) * x))", "answer": false}
|
| 110 |
+
{"id": "hard_0110", "index": 110, "difficulty": "hard", "eq1_id": 4574, "eq2_id": 4438, "equation1": "x * (y * z) = (w * w) * z", "equation2": "x * (y * x) = (x * z) * x", "answer": false}
|
| 111 |
+
{"id": "hard_0111", "index": 111, "difficulty": "hard", "eq1_id": 298, "eq2_id": 1045, "equation1": "x = ((y * z) * z) * x", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 112 |
+
{"id": "hard_0112", "index": 112, "difficulty": "hard", "eq1_id": 3184, "eq2_id": 1288, "equation1": "x = (((y * z) * x) * z) * x", "equation2": "x = y * (((x * y) * y) * x)", "answer": true}
|
| 113 |
+
{"id": "hard_0113", "index": 113, "difficulty": "hard", "eq1_id": 447, "eq2_id": 1247, "equation1": "x = x * (y * (z * (x * y)))", "equation2": "x = x * (((y * x) * z) * w)", "answer": true}
|
| 114 |
+
{"id": "hard_0114", "index": 114, "difficulty": "hard", "eq1_id": 2116, "eq2_id": 2327, "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * (x * x))) * x", "answer": false}
|
| 115 |
+
{"id": "hard_0115", "index": 115, "difficulty": "hard", "eq1_id": 302, "eq2_id": 1217, "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * ((z * (w * u)) * x)", "answer": true}
|
| 116 |
+
{"id": "hard_0116", "index": 116, "difficulty": "hard", "eq1_id": 862, "eq2_id": 2466, "equation1": "x = x * ((y * z) * (z * z))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": true}
|
| 117 |
+
{"id": "hard_0117", "index": 117, "difficulty": "hard", "eq1_id": 59, "eq2_id": 2240, "equation1": "x = x * (y * (z * y))", "equation2": "x = (x * (x * (x * y))) * x", "answer": true}
|
| 118 |
+
{"id": "hard_0118", "index": 118, "difficulty": "hard", "eq1_id": 2180, "eq2_id": 3116, "equation1": "x = ((y * z) * y) * (x * z)", "equation2": "x = (((y * x) * y) * y) * y", "answer": false}
|
| 119 |
+
{"id": "hard_0119", "index": 119, "difficulty": "hard", "eq1_id": 1927, "eq2_id": 3409, "equation1": "x = (y * (y * x)) * (z * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
|
| 120 |
+
{"id": "hard_0120", "index": 120, "difficulty": "hard", "eq1_id": 3478, "eq2_id": 4316, "equation1": "x * x = y * ((x * z) * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 121 |
+
{"id": "hard_0121", "index": 121, "difficulty": "hard", "eq1_id": 286, "eq2_id": 532, "equation1": "x = ((y * y) * z) * x", "equation2": "x = y * (y * (z * (w * x)))", "answer": true}
|
| 122 |
+
{"id": "hard_0122", "index": 122, "difficulty": "hard", "eq1_id": 2105, "eq2_id": 1229, "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 123 |
+
{"id": "hard_0123", "index": 123, "difficulty": "hard", "eq1_id": 3926, "eq2_id": 3920, "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 124 |
+
{"id": "hard_0124", "index": 124, "difficulty": "hard", "eq1_id": 4508, "eq2_id": 4527, "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 125 |
+
{"id": "hard_0125", "index": 125, "difficulty": "hard", "eq1_id": 907, "eq2_id": 221, "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 126 |
+
{"id": "hard_0126", "index": 126, "difficulty": "hard", "eq1_id": 3961, "eq2_id": 3722, "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 127 |
+
{"id": "hard_0127", "index": 127, "difficulty": "hard", "eq1_id": 164, "eq2_id": 3470, "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 128 |
+
{"id": "hard_0128", "index": 128, "difficulty": "hard", "eq1_id": 706, "eq2_id": 860, "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 129 |
+
{"id": "hard_0129", "index": 129, "difficulty": "hard", "eq1_id": 3008, "eq2_id": 1131, "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 130 |
+
{"id": "hard_0130", "index": 130, "difficulty": "hard", "eq1_id": 2890, "eq2_id": 3261, "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 131 |
+
{"id": "hard_0131", "index": 131, "difficulty": "hard", "eq1_id": 54, "eq2_id": 2695, "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 132 |
+
{"id": "hard_0132", "index": 132, "difficulty": "hard", "eq1_id": 3583, "eq2_id": 4406, "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 133 |
+
{"id": "hard_0133", "index": 133, "difficulty": "hard", "eq1_id": 1738, "eq2_id": 3972, "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 134 |
+
{"id": "hard_0134", "index": 134, "difficulty": "hard", "eq1_id": 2301, "eq2_id": 4303, "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 135 |
+
{"id": "hard_0135", "index": 135, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 900, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 136 |
+
{"id": "hard_0136", "index": 136, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 404, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 137 |
+
{"id": "hard_0137", "index": 137, "difficulty": "hard", "eq1_id": 2994, "eq2_id": 2623, "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 138 |
+
{"id": "hard_0138", "index": 138, "difficulty": "hard", "eq1_id": 386, "eq2_id": 3639, "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 139 |
+
{"id": "hard_0139", "index": 139, "difficulty": "hard", "eq1_id": 868, "eq2_id": 2243, "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 140 |
+
{"id": "hard_0140", "index": 140, "difficulty": "hard", "eq1_id": 3290, "eq2_id": 3264, "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 141 |
+
{"id": "hard_0141", "index": 141, "difficulty": "hard", "eq1_id": 1336, "eq2_id": 419, "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 142 |
+
{"id": "hard_0142", "index": 142, "difficulty": "hard", "eq1_id": 3919, "eq2_id": 3330, "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 143 |
+
{"id": "hard_0143", "index": 143, "difficulty": "hard", "eq1_id": 830, "eq2_id": 1229, "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 144 |
+
{"id": "hard_0144", "index": 144, "difficulty": "hard", "eq1_id": 1070, "eq2_id": 3950, "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 145 |
+
{"id": "hard_0145", "index": 145, "difficulty": "hard", "eq1_id": 3118, "eq2_id": 3441, "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 146 |
+
{"id": "hard_0146", "index": 146, "difficulty": "hard", "eq1_id": 168, "eq2_id": 431, "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 147 |
+
{"id": "hard_0147", "index": 147, "difficulty": "hard", "eq1_id": 3277, "eq2_id": 3473, "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 148 |
+
{"id": "hard_0148", "index": 148, "difficulty": "hard", "eq1_id": 234, "eq2_id": 3065, "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
| 149 |
+
{"id": "hard_0149", "index": 149, "difficulty": "hard", "eq1_id": 1480, "eq2_id": 1882, "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = (x * (y * z)) * (w * w)", "answer": false}
|
| 150 |
+
{"id": "hard_0150", "index": 150, "difficulty": "hard", "eq1_id": 3550, "eq2_id": 3282, "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = y * (y * (y * y))", "answer": true}
|
| 151 |
+
{"id": "hard_0151", "index": 151, "difficulty": "hard", "eq1_id": 1486, "eq2_id": 913, "equation1": "x = (y * x) * (x * (z * z))", "equation2": "x = y * ((y * x) * (z * y))", "answer": false}
|
| 152 |
+
{"id": "hard_0152", "index": 152, "difficulty": "hard", "eq1_id": 242, "eq2_id": 3197, "equation1": "x = (y * (z * y)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": false}
|
| 153 |
+
{"id": "hard_0153", "index": 153, "difficulty": "hard", "eq1_id": 4541, "eq2_id": 4578, "equation1": "x * (y * z) = (z * x) * y", "equation2": "x * (y * z) = (w * u) * y", "answer": false}
|
| 154 |
+
{"id": "hard_0154", "index": 154, "difficulty": "hard", "eq1_id": 1274, "eq2_id": 2647, "equation1": "x = x * (((y * z) * w) * u)", "equation2": "x = ((x * x) * (x * y)) * y", "answer": true}
|
| 155 |
+
{"id": "hard_0155", "index": 155, "difficulty": "hard", "eq1_id": 4150, "eq2_id": 4243, "equation1": "x * y = ((x * z) * w) * y", "equation2": "x * y = ((z * w) * x) * y", "answer": false}
|
| 156 |
+
{"id": "hard_0156", "index": 156, "difficulty": "hard", "eq1_id": 169, "eq2_id": 2056, "equation1": "x = (y * x) * (y * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
|
| 157 |
+
{"id": "hard_0157", "index": 157, "difficulty": "hard", "eq1_id": 3738, "eq2_id": 3727, "equation1": "x * y = (x * z) * (y * w)", "equation2": "x * y = (x * y) * (z * x)", "answer": false}
|
| 158 |
+
{"id": "hard_0158", "index": 158, "difficulty": "hard", "eq1_id": 4246, "eq2_id": 4469, "equation1": "x * y = ((z * w) * x) * u", "equation2": "x * (y * y) = (x * x) * x", "answer": true}
|
| 159 |
+
{"id": "hard_0159", "index": 159, "difficulty": "hard", "eq1_id": 1400, "eq2_id": 1364, "equation1": "x = y * (((z * w) * x) * x)", "equation2": "x = y * (((z * x) * w) * w)", "answer": false}
|
| 160 |
+
{"id": "hard_0160", "index": 160, "difficulty": "hard", "eq1_id": 1953, "eq2_id": 608, "equation1": "x = (y * (y * z)) * (w * x)", "equation2": "x = y * (z * (w * (u * x)))", "answer": true}
|
| 161 |
+
{"id": "hard_0161", "index": 161, "difficulty": "hard", "eq1_id": 964, "eq2_id": 698, "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x = y * (x * ((z * w) * x))", "answer": false}
|
| 162 |
+
{"id": "hard_0162", "index": 162, "difficulty": "hard", "eq1_id": 4574, "eq2_id": 4438, "equation1": "x * (y * z) = (w * w) * z", "equation2": "x * (y * x) = (x * z) * x", "answer": false}
|
| 163 |
+
{"id": "hard_0163", "index": 163, "difficulty": "hard", "eq1_id": 298, "eq2_id": 1045, "equation1": "x = ((y * z) * z) * x", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 164 |
+
{"id": "hard_0164", "index": 164, "difficulty": "hard", "eq1_id": 3184, "eq2_id": 1288, "equation1": "x = (((y * z) * x) * z) * x", "equation2": "x = y * (((x * y) * y) * x)", "answer": true}
|
| 165 |
+
{"id": "hard_0165", "index": 165, "difficulty": "hard", "eq1_id": 447, "eq2_id": 1247, "equation1": "x = x * (y * (z * (x * y)))", "equation2": "x = x * (((y * x) * z) * w)", "answer": true}
|
| 166 |
+
{"id": "hard_0166", "index": 166, "difficulty": "hard", "eq1_id": 2116, "eq2_id": 2327, "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * (x * x))) * x", "answer": false}
|
| 167 |
+
{"id": "hard_0167", "index": 167, "difficulty": "hard", "eq1_id": 302, "eq2_id": 1217, "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * ((z * (w * u)) * x)", "answer": true}
|
| 168 |
+
{"id": "hard_0168", "index": 168, "difficulty": "hard", "eq1_id": 862, "eq2_id": 2466, "equation1": "x = x * ((y * z) * (z * z))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": true}
|
| 169 |
+
{"id": "hard_0169", "index": 169, "difficulty": "hard", "eq1_id": 59, "eq2_id": 2240, "equation1": "x = x * (y * (z * y))", "equation2": "x = (x * (x * (x * y))) * x", "answer": true}
|
| 170 |
+
{"id": "hard_0170", "index": 170, "difficulty": "hard", "eq1_id": 2180, "eq2_id": 3116, "equation1": "x = ((y * z) * y) * (x * z)", "equation2": "x = (((y * x) * y) * y) * y", "answer": false}
|
| 171 |
+
{"id": "hard_0171", "index": 171, "difficulty": "hard", "eq1_id": 1927, "eq2_id": 3409, "equation1": "x = (y * (y * x)) * (z * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
|
| 172 |
+
{"id": "hard_0172", "index": 172, "difficulty": "hard", "eq1_id": 3478, "eq2_id": 4316, "equation1": "x * x = y * ((x * z) * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 173 |
+
{"id": "hard_0173", "index": 173, "difficulty": "hard", "eq1_id": 286, "eq2_id": 532, "equation1": "x = ((y * y) * z) * x", "equation2": "x = y * (y * (z * (w * x)))", "answer": true}
|
| 174 |
+
{"id": "hard_0174", "index": 174, "difficulty": "hard", "eq1_id": 2105, "eq2_id": 1229, "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 175 |
+
{"id": "hard_0175", "index": 175, "difficulty": "hard", "eq1_id": 3926, "eq2_id": 3920, "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 176 |
+
{"id": "hard_0176", "index": 176, "difficulty": "hard", "eq1_id": 4508, "eq2_id": 4527, "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 177 |
+
{"id": "hard_0177", "index": 177, "difficulty": "hard", "eq1_id": 907, "eq2_id": 221, "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 178 |
+
{"id": "hard_0178", "index": 178, "difficulty": "hard", "eq1_id": 3961, "eq2_id": 3722, "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 179 |
+
{"id": "hard_0179", "index": 179, "difficulty": "hard", "eq1_id": 164, "eq2_id": 3470, "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 180 |
+
{"id": "hard_0180", "index": 180, "difficulty": "hard", "eq1_id": 706, "eq2_id": 860, "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 181 |
+
{"id": "hard_0181", "index": 181, "difficulty": "hard", "eq1_id": 3008, "eq2_id": 1131, "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 182 |
+
{"id": "hard_0182", "index": 182, "difficulty": "hard", "eq1_id": 2890, "eq2_id": 3261, "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 183 |
+
{"id": "hard_0183", "index": 183, "difficulty": "hard", "eq1_id": 54, "eq2_id": 2695, "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 184 |
+
{"id": "hard_0184", "index": 184, "difficulty": "hard", "eq1_id": 3583, "eq2_id": 4406, "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 185 |
+
{"id": "hard_0185", "index": 185, "difficulty": "hard", "eq1_id": 1738, "eq2_id": 3972, "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 186 |
+
{"id": "hard_0186", "index": 186, "difficulty": "hard", "eq1_id": 2301, "eq2_id": 4303, "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 187 |
+
{"id": "hard_0187", "index": 187, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 900, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 188 |
+
{"id": "hard_0188", "index": 188, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 404, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 189 |
+
{"id": "hard_0189", "index": 189, "difficulty": "hard", "eq1_id": 2994, "eq2_id": 2623, "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 190 |
+
{"id": "hard_0190", "index": 190, "difficulty": "hard", "eq1_id": 386, "eq2_id": 3639, "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 191 |
+
{"id": "hard_0191", "index": 191, "difficulty": "hard", "eq1_id": 868, "eq2_id": 2243, "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 192 |
+
{"id": "hard_0192", "index": 192, "difficulty": "hard", "eq1_id": 3290, "eq2_id": 3264, "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 193 |
+
{"id": "hard_0193", "index": 193, "difficulty": "hard", "eq1_id": 1336, "eq2_id": 419, "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 194 |
+
{"id": "hard_0194", "index": 194, "difficulty": "hard", "eq1_id": 3919, "eq2_id": 3330, "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 195 |
+
{"id": "hard_0195", "index": 195, "difficulty": "hard", "eq1_id": 830, "eq2_id": 1229, "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 196 |
+
{"id": "hard_0196", "index": 196, "difficulty": "hard", "eq1_id": 1070, "eq2_id": 3950, "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 197 |
+
{"id": "hard_0197", "index": 197, "difficulty": "hard", "eq1_id": 3118, "eq2_id": 3441, "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 198 |
+
{"id": "hard_0198", "index": 198, "difficulty": "hard", "eq1_id": 168, "eq2_id": 431, "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 199 |
+
{"id": "hard_0199", "index": 199, "difficulty": "hard", "eq1_id": 3277, "eq2_id": 3473, "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 200 |
+
{"id": "hard_0200", "index": 200, "difficulty": "hard", "eq1_id": 234, "eq2_id": 3065, "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
data/hard1.jsonl
CHANGED
|
@@ -1,69 +1,69 @@
|
|
| 1 |
-
{"id": "hard1_0001", "index": 1, "difficulty": "hard", "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x * y = ((z * x) * w) * y", "answer": false}
|
| 2 |
-
{"id": "hard1_0002", "index": 2, "difficulty": "hard", "equation1": "x * (y * z) = (z * w) * w", "equation2": "x * (y * x) = (x * y) * z", "answer": false}
|
| 3 |
-
{"id": "hard1_0003", "index": 3, "difficulty": "hard", "equation1": "x = ((y * y) * z) * x", "equation2": "x = x * (((y * x) * x) * x)", "answer": true}
|
| 4 |
-
{"id": "hard1_0004", "index": 4, "difficulty": "hard", "equation1": "(x * y) * x = (x * z) * w", "equation2": "x * (y * y) = x * (z * y)", "answer": false}
|
| 5 |
-
{"id": "hard1_0005", "index": 5, "difficulty": "hard", "equation1": "x = ((y * z) * (z * x)) * y", "equation2": "x * x = (y * (y * y)) * y", "answer": false}
|
| 6 |
-
{"id": "hard1_0006", "index": 6, "difficulty": "hard", "equation1": "x * x = (x * y) * z", "equation2": "x * x = (y * z) * w", "answer": false}
|
| 7 |
-
{"id": "hard1_0007", "index": 7, "difficulty": "hard", "equation1": "x = (y * (y * (y * z))) * x", "equation2": "x * y = z * (w * (w * y))", "answer": true}
|
| 8 |
-
{"id": "hard1_0008", "index": 8, "difficulty": "hard", "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x = x * ((x * (x * x)) * x)", "answer": false}
|
| 9 |
-
{"id": "hard1_0009", "index": 9, "difficulty": "hard", "equation1": "x = ((x * x) * (y * z)) * y", "equation2": "x = ((x * (y * x)) * x) * y", "answer": false}
|
| 10 |
-
{"id": "hard1_0010", "index": 10, "difficulty": "hard", "equation1": "(x * x) * y = (y * y) * z", "equation2": "x * (y * y) = x * (z * z)", "answer": false}
|
| 11 |
-
{"id": "hard1_0011", "index": 11, "difficulty": "hard", "equation1": "x = (x * (y * z)) * (w * y)", "equation2": "x = (y * (z * w)) * (u * z)", "answer": false}
|
| 12 |
-
{"id": "hard1_0012", "index": 12, "difficulty": "hard", "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * x) = x * (y * y)", "answer": false}
|
| 13 |
-
{"id": "hard1_0013", "index": 13, "difficulty": "hard", "equation1": "x * y = ((z * y) * x) * x", "equation2": "x * y = y * (y * (y * y))", "answer": true}
|
| 14 |
-
{"id": "hard1_0014", "index": 14, "difficulty": "hard", "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = y * (z * (z * (x * y)))", "answer": false}
|
| 15 |
-
{"id": "hard1_0015", "index": 15, "difficulty": "hard", "equation1": "x * x = x * (y * (z * y))", "equation2": "x * (x * x) = x * (y * x)", "answer": false}
|
| 16 |
-
{"id": "hard1_0016", "index": 16, "difficulty": "hard", "equation1": "x = (x * y) * (x * (y * z))", "equation2": "x = (x * y) * (x * (z * y))", "answer": false}
|
| 17 |
-
{"id": "hard1_0017", "index": 17, "difficulty": "hard", "equation1": "x = y * (((x * y) * x) * y)", "equation2": "x = ((x * (y * z)) * z) * y", "answer": false}
|
| 18 |
-
{"id": "hard1_0018", "index": 18, "difficulty": "hard", "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 19 |
-
{"id": "hard1_0019", "index": 19, "difficulty": "hard", "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 20 |
-
{"id": "hard1_0020", "index": 20, "difficulty": "hard", "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 21 |
-
{"id": "hard1_0021", "index": 21, "difficulty": "hard", "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 22 |
-
{"id": "hard1_0022", "index": 22, "difficulty": "hard", "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 23 |
-
{"id": "hard1_0023", "index": 23, "difficulty": "hard", "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 24 |
-
{"id": "hard1_0024", "index": 24, "difficulty": "hard", "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 25 |
-
{"id": "hard1_0025", "index": 25, "difficulty": "hard", "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 26 |
-
{"id": "hard1_0026", "index": 26, "difficulty": "hard", "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 27 |
-
{"id": "hard1_0027", "index": 27, "difficulty": "hard", "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 28 |
-
{"id": "hard1_0028", "index": 28, "difficulty": "hard", "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 29 |
-
{"id": "hard1_0029", "index": 29, "difficulty": "hard", "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 30 |
-
{"id": "hard1_0030", "index": 30, "difficulty": "hard", "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 31 |
-
{"id": "hard1_0031", "index": 31, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 32 |
-
{"id": "hard1_0032", "index": 32, "difficulty": "hard", "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 33 |
-
{"id": "hard1_0033", "index": 33, "difficulty": "hard", "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 34 |
-
{"id": "hard1_0034", "index": 34, "difficulty": "hard", "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 35 |
-
{"id": "hard1_0035", "index": 35, "difficulty": "hard", "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 36 |
-
{"id": "hard1_0036", "index": 36, "difficulty": "hard", "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 37 |
-
{"id": "hard1_0037", "index": 37, "difficulty": "hard", "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 38 |
-
{"id": "hard1_0038", "index": 38, "difficulty": "hard", "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 39 |
-
{"id": "hard1_0039", "index": 39, "difficulty": "hard", "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 40 |
-
{"id": "hard1_0040", "index": 40, "difficulty": "hard", "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 41 |
-
{"id": "hard1_0041", "index": 41, "difficulty": "hard", "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 42 |
-
{"id": "hard1_0042", "index": 42, "difficulty": "hard", "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 43 |
-
{"id": "hard1_0043", "index": 43, "difficulty": "hard", "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 44 |
-
{"id": "hard1_0044", "index": 44, "difficulty": "hard", "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
| 45 |
-
{"id": "hard1_0045", "index": 45, "difficulty": "hard", "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = (x * (y * z)) * (w * w)", "answer": false}
|
| 46 |
-
{"id": "hard1_0046", "index": 46, "difficulty": "hard", "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = y * (y * (y * y))", "answer": true}
|
| 47 |
-
{"id": "hard1_0047", "index": 47, "difficulty": "hard", "equation1": "x = (y * x) * (x * (z * z))", "equation2": "x = y * ((y * x) * (z * y))", "answer": false}
|
| 48 |
-
{"id": "hard1_0048", "index": 48, "difficulty": "hard", "equation1": "x = (y * (z * y)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": false}
|
| 49 |
-
{"id": "hard1_0049", "index": 49, "difficulty": "hard", "equation1": "x * (y * z) = (z * x) * y", "equation2": "x * (y * z) = (w * u) * y", "answer": false}
|
| 50 |
-
{"id": "hard1_0050", "index": 50, "difficulty": "hard", "equation1": "x = x * (((y * z) * w) * u)", "equation2": "x = ((x * x) * (x * y)) * y", "answer": true}
|
| 51 |
-
{"id": "hard1_0051", "index": 51, "difficulty": "hard", "equation1": "x * y = ((x * z) * w) * y", "equation2": "x * y = ((z * w) * x) * y", "answer": false}
|
| 52 |
-
{"id": "hard1_0052", "index": 52, "difficulty": "hard", "equation1": "x = (y * x) * (y * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
|
| 53 |
-
{"id": "hard1_0053", "index": 53, "difficulty": "hard", "equation1": "x * y = (x * z) * (y * w)", "equation2": "x * y = (x * y) * (z * x)", "answer": false}
|
| 54 |
-
{"id": "hard1_0054", "index": 54, "difficulty": "hard", "equation1": "x * y = ((z * w) * x) * u", "equation2": "x * (y * y) = (x * x) * x", "answer": true}
|
| 55 |
-
{"id": "hard1_0055", "index": 55, "difficulty": "hard", "equation1": "x = y * (((z * w) * x) * x)", "equation2": "x = y * (((z * x) * w) * w)", "answer": false}
|
| 56 |
-
{"id": "hard1_0056", "index": 56, "difficulty": "hard", "equation1": "x = (y * (y * z)) * (w * x)", "equation2": "x = y * (z * (w * (u * x)))", "answer": true}
|
| 57 |
-
{"id": "hard1_0057", "index": 57, "difficulty": "hard", "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x = y * (x * ((z * w) * x))", "answer": false}
|
| 58 |
-
{"id": "hard1_0058", "index": 58, "difficulty": "hard", "equation1": "x * (y * z) = (w * w) * z", "equation2": "x * (y * x) = (x * z) * x", "answer": false}
|
| 59 |
-
{"id": "hard1_0059", "index": 59, "difficulty": "hard", "equation1": "x = ((y * z) * z) * x", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 60 |
-
{"id": "hard1_0060", "index": 60, "difficulty": "hard", "equation1": "x = (((y * z) * x) * z) * x", "equation2": "x = y * (((x * y) * y) * x)", "answer": true}
|
| 61 |
-
{"id": "hard1_0061", "index": 61, "difficulty": "hard", "equation1": "x = x * (y * (z * (x * y)))", "equation2": "x = x * (((y * x) * z) * w)", "answer": true}
|
| 62 |
-
{"id": "hard1_0062", "index": 62, "difficulty": "hard", "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * (x * x))) * x", "answer": false}
|
| 63 |
-
{"id": "hard1_0063", "index": 63, "difficulty": "hard", "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * ((z * (w * u)) * x)", "answer": true}
|
| 64 |
-
{"id": "hard1_0064", "index": 64, "difficulty": "hard", "equation1": "x = x * ((y * z) * (z * z))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": true}
|
| 65 |
-
{"id": "hard1_0065", "index": 65, "difficulty": "hard", "equation1": "x = x * (y * (z * y))", "equation2": "x = (x * (x * (x * y))) * x", "answer": true}
|
| 66 |
-
{"id": "hard1_0066", "index": 66, "difficulty": "hard", "equation1": "x = ((y * z) * y) * (x * z)", "equation2": "x = (((y * x) * y) * y) * y", "answer": false}
|
| 67 |
-
{"id": "hard1_0067", "index": 67, "difficulty": "hard", "equation1": "x = (y * (y * x)) * (z * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
|
| 68 |
-
{"id": "hard1_0068", "index": 68, "difficulty": "hard", "equation1": "x * x = y * ((x * z) * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 69 |
-
{"id": "hard1_0069", "index": 69, "difficulty": "hard", "equation1": "x = ((y * y) * z) * x", "equation2": "x = y * (y * (z * (w * x)))", "answer": true}
|
|
|
|
| 1 |
+
{"id": "hard1_0001", "index": 1, "difficulty": "hard", "eq1_id": 706, "eq2_id": 4204, "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x * y = ((z * x) * w) * y", "answer": false}
|
| 2 |
+
{"id": "hard1_0002", "index": 2, "difficulty": "hard", "eq1_id": 4555, "eq2_id": 4437, "equation1": "x * (y * z) = (z * w) * w", "equation2": "x * (y * x) = (x * y) * z", "answer": false}
|
| 3 |
+
{"id": "hard1_0003", "index": 3, "difficulty": "hard", "eq1_id": 286, "eq2_id": 1238, "equation1": "x = ((y * y) * z) * x", "equation2": "x = x * (((y * x) * x) * x)", "answer": true}
|
| 4 |
+
{"id": "hard1_0004", "index": 4, "difficulty": "hard", "eq1_id": 4634, "eq2_id": 4340, "equation1": "(x * y) * x = (x * z) * w", "equation2": "x * (y * y) = x * (z * y)", "answer": false}
|
| 5 |
+
{"id": "hard1_0005", "index": 5, "difficulty": "hard", "eq1_id": 2805, "eq2_id": 3891, "equation1": "x = ((y * z) * (z * x)) * y", "equation2": "x * x = (y * (y * y)) * y", "answer": false}
|
| 6 |
+
{"id": "hard1_0006", "index": 6, "difficulty": "hard", "eq1_id": 363, "eq2_id": 373, "equation1": "x * x = (x * y) * z", "equation2": "x * x = (y * z) * w", "answer": false}
|
| 7 |
+
{"id": "hard1_0007", "index": 7, "difficulty": "hard", "eq1_id": 2343, "eq2_id": 3446, "equation1": "x = (y * (y * (y * z))) * x", "equation2": "x * y = z * (w * (w * y))", "answer": true}
|
| 8 |
+
{"id": "hard1_0008", "index": 8, "difficulty": "hard", "eq1_id": 646, "eq2_id": 1020, "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x = x * ((x * (x * x)) * x)", "answer": false}
|
| 9 |
+
{"id": "hard1_0009", "index": 9, "difficulty": "hard", "eq1_id": 2656, "eq2_id": 2863, "equation1": "x = ((x * x) * (y * z)) * y", "equation2": "x = ((x * (y * x)) * x) * y", "answer": false}
|
| 10 |
+
{"id": "hard1_0010", "index": 10, "difficulty": "hard", "eq1_id": 4609, "eq2_id": 4341, "equation1": "(x * x) * y = (y * y) * z", "equation2": "x * (y * y) = x * (z * z)", "answer": false}
|
| 11 |
+
{"id": "hard1_0011", "index": 11, "difficulty": "hard", "eq1_id": 1880, "eq2_id": 2031, "equation1": "x = (x * (y * z)) * (w * y)", "equation2": "x = (y * (z * w)) * (u * z)", "answer": false}
|
| 12 |
+
{"id": "hard1_0012", "index": 12, "difficulty": "hard", "eq1_id": 4653, "eq2_id": 4270, "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * x) = x * (y * y)", "answer": false}
|
| 13 |
+
{"id": "hard1_0013", "index": 13, "difficulty": "hard", "eq1_id": 4208, "eq2_id": 3356, "equation1": "x * y = ((z * y) * x) * x", "equation2": "x * y = y * (y * (y * y))", "answer": true}
|
| 14 |
+
{"id": "hard1_0014", "index": 14, "difficulty": "hard", "eq1_id": 1480, "eq2_id": 572, "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = y * (z * (z * (x * y)))", "answer": false}
|
| 15 |
+
{"id": "hard1_0015", "index": 15, "difficulty": "hard", "eq1_id": 3265, "eq2_id": 4269, "equation1": "x * x = x * (y * (z * y))", "equation2": "x * (x * x) = x * (y * x)", "answer": false}
|
| 16 |
+
{"id": "hard1_0016", "index": 16, "difficulty": "hard", "eq1_id": 1446, "eq2_id": 1448, "equation1": "x = (x * y) * (x * (y * z))", "equation2": "x = (x * y) * (x * (z * y))", "answer": false}
|
| 17 |
+
{"id": "hard1_0017", "index": 17, "difficulty": "hard", "eq1_id": 1286, "eq2_id": 2891, "equation1": "x = y * (((x * y) * x) * y)", "equation2": "x = ((x * (y * z)) * z) * y", "answer": false}
|
| 18 |
+
{"id": "hard1_0018", "index": 18, "difficulty": "hard", "eq1_id": 2105, "eq2_id": 1229, "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = x * (((x * y) * x) * y)", "answer": true}
|
| 19 |
+
{"id": "hard1_0019", "index": 19, "difficulty": "hard", "eq1_id": 3926, "eq2_id": 3920, "equation1": "x * y = (x * (y * x)) * z", "equation2": "x * y = (x * (x * z)) * x", "answer": false}
|
| 20 |
+
{"id": "hard1_0020", "index": 20, "difficulty": "hard", "eq1_id": 4508, "eq2_id": 4527, "equation1": "x * (y * z) = (x * x) * z", "equation2": "x * (y * z) = (y * y) * x", "answer": false}
|
| 21 |
+
{"id": "hard1_0021", "index": 21, "difficulty": "hard", "eq1_id": 907, "eq2_id": 221, "equation1": "x = y * ((y * x) * (x * y))", "equation2": "x = (y * (x * y)) * x", "answer": false}
|
| 22 |
+
{"id": "hard1_0022", "index": 22, "difficulty": "hard", "eq1_id": 3961, "eq2_id": 3722, "equation1": "x * y = (y * (y * x)) * x", "equation2": "x * y = (x * y) * (x * y)", "answer": false}
|
| 23 |
+
{"id": "hard1_0023", "index": 23, "difficulty": "hard", "eq1_id": 164, "eq2_id": 3470, "equation1": "x = (x * y) * (z * z)", "equation2": "x * x = x * ((y * z) * w)", "answer": true}
|
| 24 |
+
{"id": "hard1_0024", "index": 24, "difficulty": "hard", "eq1_id": 706, "eq2_id": 860, "equation1": "x = y * (y * ((x * y) * x))", "equation2": "x = x * ((y * z) * (z * x))", "answer": false}
|
| 25 |
+
{"id": "hard1_0025", "index": 25, "difficulty": "hard", "eq1_id": 3008, "eq2_id": 1131, "equation1": "x = ((y * (z * z)) * x) * y", "equation2": "x = y * ((y * (z * x)) * z)", "answer": false}
|
| 26 |
+
{"id": "hard1_0026", "index": 26, "difficulty": "hard", "eq1_id": 2890, "eq2_id": 3261, "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x * x = x * (y * (y * x))", "answer": false}
|
| 27 |
+
{"id": "hard1_0027", "index": 27, "difficulty": "hard", "eq1_id": 54, "eq2_id": 2695, "equation1": "x = x * (y * (x * z))", "equation2": "x = ((x * y) * (z * w)) * u", "answer": true}
|
| 28 |
+
{"id": "hard1_0028", "index": 28, "difficulty": "hard", "eq1_id": 3583, "eq2_id": 4406, "equation1": "x * y = z * ((x * x) * y)", "equation2": "x * (x * y) = (y * x) * y", "answer": false}
|
| 29 |
+
{"id": "hard1_0029", "index": 29, "difficulty": "hard", "eq1_id": 1738, "eq2_id": 3972, "equation1": "x = (y * y) * ((z * x) * x)", "equation2": "x * y = (y * (z * x)) * y", "answer": false}
|
| 30 |
+
{"id": "hard1_0030", "index": 30, "difficulty": "hard", "eq1_id": 2301, "eq2_id": 4303, "equation1": "x = (y * (x * (y * x))) * y", "equation2": "x * (x * y) = z * (y * x)", "answer": false}
|
| 31 |
+
{"id": "hard1_0031", "index": 31, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 900, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x = y * ((x * z) * (z * w))", "answer": false}
|
| 32 |
+
{"id": "hard1_0032", "index": 32, "difficulty": "hard", "eq1_id": 2089, "eq2_id": 404, "equation1": "x = ((y * x) * x) * (x * z)", "equation2": "x * y = (z * z) * z", "answer": false}
|
| 33 |
+
{"id": "hard1_0033", "index": 33, "difficulty": "hard", "eq1_id": 2994, "eq2_id": 2623, "equation1": "x = ((y * (z * y)) * y) * x", "equation2": "x = (y * ((z * w) * y)) * x", "answer": false}
|
| 34 |
+
{"id": "hard1_0034", "index": 34, "difficulty": "hard", "eq1_id": 386, "eq2_id": 3639, "equation1": "x * y = (y * x) * z", "equation2": "x * y = z * ((w * y) * y)", "answer": true}
|
| 35 |
+
{"id": "hard1_0035", "index": 35, "difficulty": "hard", "eq1_id": 868, "eq2_id": 2243, "equation1": "x = x * ((y * z) * (w * u))", "equation2": "x = (x * (x * (y * x))) * x", "answer": true}
|
| 36 |
+
{"id": "hard1_0036", "index": 36, "difficulty": "hard", "eq1_id": 3290, "eq2_id": 3264, "equation1": "x * x = y * (z * (x * z))", "equation2": "x * x = x * (y * (z * x))", "answer": false}
|
| 37 |
+
{"id": "hard1_0037", "index": 37, "difficulty": "hard", "eq1_id": 1336, "eq2_id": 419, "equation1": "x = y * (((y * z) * y) * x)", "equation2": "x = x * (x * (y * (y * x)))", "answer": false}
|
| 38 |
+
{"id": "hard1_0038", "index": 38, "difficulty": "hard", "eq1_id": 3919, "eq2_id": 3330, "equation1": "x * y = (x * (x * y)) * z", "equation2": "x * y = x * (z * (y * y))", "answer": false}
|
| 39 |
+
{"id": "hard1_0039", "index": 39, "difficulty": "hard", "eq1_id": 830, "eq2_id": 1229, "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x = x * (((x * y) * x) * y)", "answer": false}
|
| 40 |
+
{"id": "hard1_0040", "index": 40, "difficulty": "hard", "eq1_id": 1070, "eq2_id": 3950, "equation1": "x = x * ((y * (z * w)) * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 41 |
+
{"id": "hard1_0041", "index": 41, "difficulty": "hard", "eq1_id": 3118, "eq2_id": 3441, "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * y = z * (w * (z * y))", "answer": true}
|
| 42 |
+
{"id": "hard1_0042", "index": 42, "difficulty": "hard", "eq1_id": 168, "eq2_id": 431, "equation1": "x = (y * x) * (x * z)", "equation2": "x = x * (y * (x * (y * z)))", "answer": false}
|
| 43 |
+
{"id": "hard1_0043", "index": 43, "difficulty": "hard", "eq1_id": 3277, "eq2_id": 3473, "equation1": "x * x = y * (x * (z * w))", "equation2": "x * x = y * ((x * x) * z)", "answer": false}
|
| 44 |
+
{"id": "hard1_0044", "index": 44, "difficulty": "hard", "eq1_id": 234, "eq2_id": 3065, "equation1": "x = (y * (y * z)) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
| 45 |
+
{"id": "hard1_0045", "index": 45, "difficulty": "hard", "eq1_id": 1480, "eq2_id": 1882, "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = (x * (y * z)) * (w * w)", "answer": false}
|
| 46 |
+
{"id": "hard1_0046", "index": 46, "difficulty": "hard", "eq1_id": 3550, "eq2_id": 3282, "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = y * (y * (y * y))", "answer": true}
|
| 47 |
+
{"id": "hard1_0047", "index": 47, "difficulty": "hard", "eq1_id": 1486, "eq2_id": 913, "equation1": "x = (y * x) * (x * (z * z))", "equation2": "x = y * ((y * x) * (z * y))", "answer": false}
|
| 48 |
+
{"id": "hard1_0048", "index": 48, "difficulty": "hard", "eq1_id": 242, "eq2_id": 3197, "equation1": "x = (y * (z * y)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": false}
|
| 49 |
+
{"id": "hard1_0049", "index": 49, "difficulty": "hard", "eq1_id": 4541, "eq2_id": 4578, "equation1": "x * (y * z) = (z * x) * y", "equation2": "x * (y * z) = (w * u) * y", "answer": false}
|
| 50 |
+
{"id": "hard1_0050", "index": 50, "difficulty": "hard", "eq1_id": 1274, "eq2_id": 2647, "equation1": "x = x * (((y * z) * w) * u)", "equation2": "x = ((x * x) * (x * y)) * y", "answer": true}
|
| 51 |
+
{"id": "hard1_0051", "index": 51, "difficulty": "hard", "eq1_id": 4150, "eq2_id": 4243, "equation1": "x * y = ((x * z) * w) * y", "equation2": "x * y = ((z * w) * x) * y", "answer": false}
|
| 52 |
+
{"id": "hard1_0052", "index": 52, "difficulty": "hard", "eq1_id": 169, "eq2_id": 2056, "equation1": "x = (y * x) * (y * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
|
| 53 |
+
{"id": "hard1_0053", "index": 53, "difficulty": "hard", "eq1_id": 3738, "eq2_id": 3727, "equation1": "x * y = (x * z) * (y * w)", "equation2": "x * y = (x * y) * (z * x)", "answer": false}
|
| 54 |
+
{"id": "hard1_0054", "index": 54, "difficulty": "hard", "eq1_id": 4246, "eq2_id": 4469, "equation1": "x * y = ((z * w) * x) * u", "equation2": "x * (y * y) = (x * x) * x", "answer": true}
|
| 55 |
+
{"id": "hard1_0055", "index": 55, "difficulty": "hard", "eq1_id": 1400, "eq2_id": 1364, "equation1": "x = y * (((z * w) * x) * x)", "equation2": "x = y * (((z * x) * w) * w)", "answer": false}
|
| 56 |
+
{"id": "hard1_0056", "index": 56, "difficulty": "hard", "eq1_id": 1953, "eq2_id": 608, "equation1": "x = (y * (y * z)) * (w * x)", "equation2": "x = y * (z * (w * (u * x)))", "answer": true}
|
| 57 |
+
{"id": "hard1_0057", "index": 57, "difficulty": "hard", "eq1_id": 964, "eq2_id": 698, "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x = y * (x * ((z * w) * x))", "answer": false}
|
| 58 |
+
{"id": "hard1_0058", "index": 58, "difficulty": "hard", "eq1_id": 4574, "eq2_id": 4438, "equation1": "x * (y * z) = (w * w) * z", "equation2": "x * (y * x) = (x * z) * x", "answer": false}
|
| 59 |
+
{"id": "hard1_0059", "index": 59, "difficulty": "hard", "eq1_id": 298, "eq2_id": 1045, "equation1": "x = ((y * z) * z) * x", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 60 |
+
{"id": "hard1_0060", "index": 60, "difficulty": "hard", "eq1_id": 3184, "eq2_id": 1288, "equation1": "x = (((y * z) * x) * z) * x", "equation2": "x = y * (((x * y) * y) * x)", "answer": true}
|
| 61 |
+
{"id": "hard1_0061", "index": 61, "difficulty": "hard", "eq1_id": 447, "eq2_id": 1247, "equation1": "x = x * (y * (z * (x * y)))", "equation2": "x = x * (((y * x) * z) * w)", "answer": true}
|
| 62 |
+
{"id": "hard1_0062", "index": 62, "difficulty": "hard", "eq1_id": 2116, "eq2_id": 2327, "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * (x * x))) * x", "answer": false}
|
| 63 |
+
{"id": "hard1_0063", "index": 63, "difficulty": "hard", "eq1_id": 302, "eq2_id": 1217, "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * ((z * (w * u)) * x)", "answer": true}
|
| 64 |
+
{"id": "hard1_0064", "index": 64, "difficulty": "hard", "eq1_id": 862, "eq2_id": 2466, "equation1": "x = x * ((y * z) * (z * z))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": true}
|
| 65 |
+
{"id": "hard1_0065", "index": 65, "difficulty": "hard", "eq1_id": 59, "eq2_id": 2240, "equation1": "x = x * (y * (z * y))", "equation2": "x = (x * (x * (x * y))) * x", "answer": true}
|
| 66 |
+
{"id": "hard1_0066", "index": 66, "difficulty": "hard", "eq1_id": 2180, "eq2_id": 3116, "equation1": "x = ((y * z) * y) * (x * z)", "equation2": "x = (((y * x) * y) * y) * y", "answer": false}
|
| 67 |
+
{"id": "hard1_0067", "index": 67, "difficulty": "hard", "eq1_id": 1927, "eq2_id": 3409, "equation1": "x = (y * (y * x)) * (z * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
|
| 68 |
+
{"id": "hard1_0068", "index": 68, "difficulty": "hard", "eq1_id": 3478, "eq2_id": 4316, "equation1": "x * x = y * ((x * z) * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 69 |
+
{"id": "hard1_0069", "index": 69, "difficulty": "hard", "eq1_id": 286, "eq2_id": 532, "equation1": "x = ((y * y) * z) * x", "equation2": "x = y * (y * (z * (w * x)))", "answer": true}
|
data/hard2.jsonl
CHANGED
|
@@ -1,200 +1,200 @@
|
|
| 1 |
-
{"id": "hard2_0001", "index": 1, "difficulty": "hard", "equation1": "x * (y * z) = (y * w) * w", "equation2": "x * (y * y) = (z * w) * u", "answer": false}
|
| 2 |
-
{"id": "hard2_0002", "index": 2, "difficulty": "hard", "equation1": "x = y * ((y * (y * x)) * x)", "equation2": "x = (y * (z * y)) * (y * x)", "answer": false}
|
| 3 |
-
{"id": "hard2_0003", "index": 3, "difficulty": "hard", "equation1": "x * y = y * (x * (z * x))", "equation2": "x * y = (y * (z * x)) * y", "answer": true}
|
| 4 |
-
{"id": "hard2_0004", "index": 4, "difficulty": "hard", "equation1": "x = (((y * y) * x) * x) * z", "equation2": "x = y * ((x * (y * z)) * w)", "answer": true}
|
| 5 |
-
{"id": "hard2_0005", "index": 5, "difficulty": "hard", "equation1": "x = y * ((z * (z * x)) * y)", "equation2": "x = (x * ((x * y) * y)) * x", "answer": true}
|
| 6 |
-
{"id": "hard2_0006", "index": 6, "difficulty": "hard", "equation1": "x = y * (z * (x * (x * w)))", "equation2": "x = ((y * y) * x) * (y * y)", "answer": true}
|
| 7 |
-
{"id": "hard2_0007", "index": 7, "difficulty": "hard", "equation1": "x * (x * y) = (z * y) * w", "equation2": "x * (x * y) = y * (z * y)", "answer": false}
|
| 8 |
-
{"id": "hard2_0008", "index": 8, "difficulty": "hard", "equation1": "x = y * (x * (x * (z * y)))", "equation2": "x = x * (x * ((y * y) * x))", "answer": true}
|
| 9 |
-
{"id": "hard2_0009", "index": 9, "difficulty": "hard", "equation1": "x = y * ((x * z) * (z * y))", "equation2": "x = ((x * y) * (y * y)) * y", "answer": false}
|
| 10 |
-
{"id": "hard2_0010", "index": 10, "difficulty": "hard", "equation1": "x = (x * y) * ((x * y) * y)", "equation2": "x = (x * (x * (x * x))) * y", "answer": false}
|
| 11 |
-
{"id": "hard2_0011", "index": 11, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = (y * (z * z)) * w", "answer": false}
|
| 12 |
-
{"id": "hard2_0012", "index": 12, "difficulty": "hard", "equation1": "x = y * (((z * y) * x) * z)", "equation2": "(x * x) * y = (y * z) * z", "answer": false}
|
| 13 |
-
{"id": "hard2_0013", "index": 13, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = x * (((x * y) * x) * z)", "answer": false}
|
| 14 |
-
{"id": "hard2_0014", "index": 14, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "(x * y) * z = (z * y) * x", "answer": false}
|
| 15 |
-
{"id": "hard2_0015", "index": 15, "difficulty": "hard", "equation1": "x * x = (y * (z * w)) * u", "equation2": "x * y = (z * z) * (x * y)", "answer": false}
|
| 16 |
-
{"id": "hard2_0016", "index": 16, "difficulty": "hard", "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x * y = ((x * y) * x) * x", "answer": false}
|
| 17 |
-
{"id": "hard2_0017", "index": 17, "difficulty": "hard", "equation1": "x = y * (x * (y * (y * z)))", "equation2": "x = ((y * (z * w)) * z) * x", "answer": true}
|
| 18 |
-
{"id": "hard2_0018", "index": 18, "difficulty": "hard", "equation1": "x = x * ((x * (y * z)) * z)", "equation2": "x = x * (x * (y * x))", "answer": true}
|
| 19 |
-
{"id": "hard2_0019", "index": 19, "difficulty": "hard", "equation1": "x = (((y * y) * z) * x) * w", "equation2": "x * y = ((y * x) * y) * y", "answer": true}
|
| 20 |
-
{"id": "hard2_0020", "index": 20, "difficulty": "hard", "equation1": "x * (y * z) = z * (w * u)", "equation2": "(x * y) * y = (x * z) * y", "answer": false}
|
| 21 |
-
{"id": "hard2_0021", "index": 21, "difficulty": "hard", "equation1": "x * y = y * ((z * w) * x)", "equation2": "(x * x) * y = (z * y) * x", "answer": true}
|
| 22 |
-
{"id": "hard2_0022", "index": 22, "difficulty": "hard", "equation1": "x = y * (((x * y) * z) * w)", "equation2": "x = (y * ((x * x) * y)) * x", "answer": true}
|
| 23 |
-
{"id": "hard2_0023", "index": 23, "difficulty": "hard", "equation1": "x = x * (y * (x * z))", "equation2": "x = (x * ((y * z) * w)) * x", "answer": true}
|
| 24 |
-
{"id": "hard2_0024", "index": 24, "difficulty": "hard", "equation1": "x = y * (z * (x * x))", "equation2": "x = y * (y * ((x * z) * x))", "answer": true}
|
| 25 |
-
{"id": "hard2_0025", "index": 25, "difficulty": "hard", "equation1": "x * y = x * ((z * y) * x)", "equation2": "x * y = x * (x * (y * y))", "answer": false}
|
| 26 |
-
{"id": "hard2_0026", "index": 26, "difficulty": "hard", "equation1": "x = (((y * x) * z) * y) * x", "equation2": "x = ((x * x) * (y * y)) * x", "answer": true}
|
| 27 |
-
{"id": "hard2_0027", "index": 27, "difficulty": "hard", "equation1": "x = y * ((z * (y * y)) * x)", "equation2": "x = (y * z) * ((x * z) * x)", "answer": false}
|
| 28 |
-
{"id": "hard2_0028", "index": 28, "difficulty": "hard", "equation1": "x * y = y * ((y * z) * x)", "equation2": "x * y = ((z * x) * y) * x", "answer": true}
|
| 29 |
-
{"id": "hard2_0029", "index": 29, "difficulty": "hard", "equation1": "x * y = ((y * y) * x) * x", "equation2": "x * y = (x * (y * y)) * x", "answer": false}
|
| 30 |
-
{"id": "hard2_0030", "index": 30, "difficulty": "hard", "equation1": "x = y * (x * ((z * z) * w))", "equation2": "x * y = ((y * x) * y) * y", "answer": true}
|
| 31 |
-
{"id": "hard2_0031", "index": 31, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = ((y * (z * w)) * u) * z", "answer": false}
|
| 32 |
-
{"id": "hard2_0032", "index": 32, "difficulty": "hard", "equation1": "x * y = (z * (x * w)) * y", "equation2": "x * x = (y * (y * y)) * x", "answer": false}
|
| 33 |
-
{"id": "hard2_0033", "index": 33, "difficulty": "hard", "equation1": "x = y * ((z * (x * x)) * y)", "equation2": "x = (y * ((x * y) * z)) * z", "answer": true}
|
| 34 |
-
{"id": "hard2_0034", "index": 34, "difficulty": "hard", "equation1": "x * y = (y * (x * z)) * z", "equation2": "x * y = y * ((z * z) * x)", "answer": false}
|
| 35 |
-
{"id": "hard2_0035", "index": 35, "difficulty": "hard", "equation1": "x = ((y * x) * (x * z)) * w", "equation2": "x = (y * (x * (y * z))) * x", "answer": true}
|
| 36 |
-
{"id": "hard2_0036", "index": 36, "difficulty": "hard", "equation1": "x = (y * (z * x)) * (x * w)", "equation2": "x = (((y * y) * y) * z) * x", "answer": true}
|
| 37 |
-
{"id": "hard2_0037", "index": 37, "difficulty": "hard", "equation1": "x = (((y * z) * w) * w) * x", "equation2": "x = x * (((y * y) * y) * x)", "answer": true}
|
| 38 |
-
{"id": "hard2_0038", "index": 38, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = y * (y * (y * (z * w)))", "answer": false}
|
| 39 |
-
{"id": "hard2_0039", "index": 39, "difficulty": "hard", "equation1": "x = y * ((y * (x * x)) * z)", "equation2": "x = ((x * (y * z)) * z) * y", "answer": true}
|
| 40 |
-
{"id": "hard2_0040", "index": 40, "difficulty": "hard", "equation1": "x = y * (x * ((y * z) * w))", "equation2": "x = x * (x * (y * x))", "answer": true}
|
| 41 |
-
{"id": "hard2_0041", "index": 41, "difficulty": "hard", "equation1": "x = y * ((y * (x * y)) * x)", "equation2": "x = (x * (y * x)) * (x * x)", "answer": false}
|
| 42 |
-
{"id": "hard2_0042", "index": 42, "difficulty": "hard", "equation1": "x * (y * x) = (z * w) * u", "equation2": "x * (y * z) = (w * x) * w", "answer": false}
|
| 43 |
-
{"id": "hard2_0043", "index": 43, "difficulty": "hard", "equation1": "x = ((x * (x * y)) * y) * y", "equation2": "x * (y * x) = x * (y * z)", "answer": false}
|
| 44 |
-
{"id": "hard2_0044", "index": 44, "difficulty": "hard", "equation1": "x = (y * ((z * z) * x)) * w", "equation2": "x = ((x * y) * (y * z)) * z", "answer": true}
|
| 45 |
-
{"id": "hard2_0045", "index": 45, "difficulty": "hard", "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = x * ((x * z) * y)", "answer": false}
|
| 46 |
-
{"id": "hard2_0046", "index": 46, "difficulty": "hard", "equation1": "(x * y) * z = (w * z) * u", "equation2": "x * (x * x) = y * (z * w)", "answer": false}
|
| 47 |
-
{"id": "hard2_0047", "index": 47, "difficulty": "hard", "equation1": "x * y = (y * (x * z)) * y", "equation2": "x * x = ((x * x) * y) * x", "answer": false}
|
| 48 |
-
{"id": "hard2_0048", "index": 48, "difficulty": "hard", "equation1": "(x * y) * z = (w * y) * u", "equation2": "x * (x * y) = z * (x * x)", "answer": false}
|
| 49 |
-
{"id": "hard2_0049", "index": 49, "difficulty": "hard", "equation1": "x = y * (((z * w) * x) * y)", "equation2": "x = x * (y * ((x * x) * x))", "answer": true}
|
| 50 |
-
{"id": "hard2_0050", "index": 50, "difficulty": "hard", "equation1": "x = y * ((z * x) * z)", "equation2": "x = ((y * (z * z)) * w) * x", "answer": true}
|
| 51 |
-
{"id": "hard2_0051", "index": 51, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x * (x * y) = z * (z * y)", "answer": false}
|
| 52 |
-
{"id": "hard2_0052", "index": 52, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = x * (y * (z * (w * y)))", "answer": false}
|
| 53 |
-
{"id": "hard2_0053", "index": 53, "difficulty": "hard", "equation1": "x = y * (x * (z * (x * z)))", "equation2": "x = ((y * y) * x) * (y * y)", "answer": true}
|
| 54 |
-
{"id": "hard2_0054", "index": 54, "difficulty": "hard", "equation1": "(x * y) * z = (y * w) * u", "equation2": "x * (y * y) = (z * y) * z", "answer": false}
|
| 55 |
-
{"id": "hard2_0055", "index": 55, "difficulty": "hard", "equation1": "x * (y * x) = (z * w) * u", "equation2": "x * (x * y) = y * (z * x)", "answer": false}
|
| 56 |
-
{"id": "hard2_0056", "index": 56, "difficulty": "hard", "equation1": "x = y * ((y * (y * x)) * x)", "equation2": "x = ((y * z) * z) * (w * x)", "answer": false}
|
| 57 |
-
{"id": "hard2_0057", "index": 57, "difficulty": "hard", "equation1": "x = y * ((z * (w * w)) * x)", "equation2": "x = ((y * z) * y) * (y * x)", "answer": true}
|
| 58 |
-
{"id": "hard2_0058", "index": 58, "difficulty": "hard", "equation1": "x = (y * z) * ((w * x) * y)", "equation2": "x = (y * (z * (y * y))) * x", "answer": true}
|
| 59 |
-
{"id": "hard2_0059", "index": 59, "difficulty": "hard", "equation1": "x = (y * x) * (z * (x * w))", "equation2": "x = y * ((x * (x * x)) * y)", "answer": true}
|
| 60 |
-
{"id": "hard2_0060", "index": 60, "difficulty": "hard", "equation1": "x = x * (y * ((x * z) * y))", "equation2": "x = x * ((y * (z * w)) * w)", "answer": true}
|
| 61 |
-
{"id": "hard2_0061", "index": 61, "difficulty": "hard", "equation1": "x = y * (((x * x) * z) * z)", "equation2": "x = y * (y * ((y * z) * w))", "answer": true}
|
| 62 |
-
{"id": "hard2_0062", "index": 62, "difficulty": "hard", "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = ((z * w) * u) * v", "answer": false}
|
| 63 |
-
{"id": "hard2_0063", "index": 63, "difficulty": "hard", "equation1": "x = y * (z * (x * z))", "equation2": "x = y * (x * ((y * y) * y))", "answer": true}
|
| 64 |
-
{"id": "hard2_0064", "index": 64, "difficulty": "hard", "equation1": "x = (y * z) * (z * (x * y))", "equation2": "x = y * (z * (y * (z * x)))", "answer": false}
|
| 65 |
-
{"id": "hard2_0065", "index": 65, "difficulty": "hard", "equation1": "x * y = z * (y * (x * x))", "equation2": "x * y = (x * (y * y)) * y", "answer": true}
|
| 66 |
-
{"id": "hard2_0066", "index": 66, "difficulty": "hard", "equation1": "x = (y * x) * ((z * w) * w)", "equation2": "x = (x * ((y * y) * y)) * x", "answer": true}
|
| 67 |
-
{"id": "hard2_0067", "index": 67, "difficulty": "hard", "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * y)) * (x * y)", "answer": false}
|
| 68 |
-
{"id": "hard2_0068", "index": 68, "difficulty": "hard", "equation1": "x * (x * y) = (z * w) * u", "equation2": "x * (y * z) = y * (x * z)", "answer": false}
|
| 69 |
-
{"id": "hard2_0069", "index": 69, "difficulty": "hard", "equation1": "x = y * (((y * x) * y) * z)", "equation2": "x = x * ((x * (x * x)) * y)", "answer": true}
|
| 70 |
-
{"id": "hard2_0070", "index": 70, "difficulty": "hard", "equation1": "x * y = y * (y * (z * x))", "equation2": "x * y = (x * (z * z)) * z", "answer": true}
|
| 71 |
-
{"id": "hard2_0071", "index": 71, "difficulty": "hard", "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = z * (y * (w * x))", "answer": false}
|
| 72 |
-
{"id": "hard2_0072", "index": 72, "difficulty": "hard", "equation1": "x = ((y * (x * x)) * z) * w", "equation2": "x = y * ((z * (w * x)) * y)", "answer": true}
|
| 73 |
-
{"id": "hard2_0073", "index": 73, "difficulty": "hard", "equation1": "x = ((y * (x * z)) * x) * y", "equation2": "x = x * (((y * y) * x) * x)", "answer": true}
|
| 74 |
-
{"id": "hard2_0074", "index": 74, "difficulty": "hard", "equation1": "x = (y * z) * (w * (x * x))", "equation2": "x = y * (z * ((z * z) * x))", "answer": true}
|
| 75 |
-
{"id": "hard2_0075", "index": 75, "difficulty": "hard", "equation1": "x = ((y * (z * z)) * x) * w", "equation2": "x = (y * (y * (z * x))) * z", "answer": true}
|
| 76 |
-
{"id": "hard2_0076", "index": 76, "difficulty": "hard", "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * y) = (z * w) * z", "answer": false}
|
| 77 |
-
{"id": "hard2_0077", "index": 77, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = (((x * y) * x) * x) * x", "answer": false}
|
| 78 |
-
{"id": "hard2_0078", "index": 78, "difficulty": "hard", "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = ((y * x) * z) * z", "answer": true}
|
| 79 |
-
{"id": "hard2_0079", "index": 79, "difficulty": "hard", "equation1": "x = (y * (x * (y * z))) * y", "equation2": "x = y * (x * ((y * y) * y))", "answer": true}
|
| 80 |
-
{"id": "hard2_0080", "index": 80, "difficulty": "hard", "equation1": "x = ((y * z) * (y * x)) * y", "equation2": "x = x * (y * ((x * y) * x))", "answer": true}
|
| 81 |
-
{"id": "hard2_0081", "index": 81, "difficulty": "hard", "equation1": "x = (y * (x * (x * z))) * w", "equation2": "x = x * (y * ((x * y) * y))", "answer": true}
|
| 82 |
-
{"id": "hard2_0082", "index": 82, "difficulty": "hard", "equation1": "x * y = y * ((z * w) * x)", "equation2": "x * y = (z * x) * (w * y)", "answer": true}
|
| 83 |
-
{"id": "hard2_0083", "index": 83, "difficulty": "hard", "equation1": "x = ((y * z) * y) * (x * x)", "equation2": "x * y = z * (w * (x * y))", "answer": true}
|
| 84 |
-
{"id": "hard2_0084", "index": 84, "difficulty": "hard", "equation1": "x * (y * z) = (z * y) * y", "equation2": "x * (y * z) = (y * z) * w", "answer": false}
|
| 85 |
-
{"id": "hard2_0085", "index": 85, "difficulty": "hard", "equation1": "x = ((y * z) * (x * w)) * u", "equation2": "x = (((y * x) * x) * y) * x", "answer": true}
|
| 86 |
-
{"id": "hard2_0086", "index": 86, "difficulty": "hard", "equation1": "x = (y * ((z * z) * x)) * w", "equation2": "x = y * (((y * x) * y) * y)", "answer": true}
|
| 87 |
-
{"id": "hard2_0087", "index": 87, "difficulty": "hard", "equation1": "x * (x * y) = (z * y) * w", "equation2": "x * (x * y) = y * (z * z)", "answer": false}
|
| 88 |
-
{"id": "hard2_0088", "index": 88, "difficulty": "hard", "equation1": "x = (x * (x * y)) * y", "equation2": "x * (y * z) = x * (z * y)", "answer": false}
|
| 89 |
-
{"id": "hard2_0089", "index": 89, "difficulty": "hard", "equation1": "x = y * (((x * x) * z) * w)", "equation2": "x = (y * (z * (w * u))) * x", "answer": true}
|
| 90 |
-
{"id": "hard2_0090", "index": 90, "difficulty": "hard", "equation1": "x * y = (y * (x * z)) * y", "equation2": "x * y = ((x * y) * x) * y", "answer": false}
|
| 91 |
-
{"id": "hard2_0091", "index": 91, "difficulty": "hard", "equation1": "x = y * (((x * z) * x) * w)", "equation2": "x = ((y * (y * y)) * x) * z", "answer": true}
|
| 92 |
-
{"id": "hard2_0092", "index": 92, "difficulty": "hard", "equation1": "x * (y * z) = (w * u) * u", "equation2": "x * (y * z) = (y * w) * u", "answer": false}
|
| 93 |
-
{"id": "hard2_0093", "index": 93, "difficulty": "hard", "equation1": "x = (y * y) * (x * (y * x))", "equation2": "x * y = (x * (x * x)) * y", "answer": false}
|
| 94 |
-
{"id": "hard2_0094", "index": 94, "difficulty": "hard", "equation1": "x = y * ((x * (x * x)) * z)", "equation2": "x = ((x * y) * z) * (w * y)", "answer": true}
|
| 95 |
-
{"id": "hard2_0095", "index": 95, "difficulty": "hard", "equation1": "x = y * ((z * (z * y)) * x)", "equation2": "x * y = (y * (y * x)) * y", "answer": false}
|
| 96 |
-
{"id": "hard2_0096", "index": 96, "difficulty": "hard", "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x * y = ((z * x) * x) * y", "answer": false}
|
| 97 |
-
{"id": "hard2_0097", "index": 97, "difficulty": "hard", "equation1": "x = (x * (x * (y * y))) * z", "equation2": "x * x = ((x * y) * z) * w", "answer": true}
|
| 98 |
-
{"id": "hard2_0098", "index": 98, "difficulty": "hard", "equation1": "x = (y * (x * (y * z))) * y", "equation2": "x = y * ((y * (x * x)) * x)", "answer": true}
|
| 99 |
-
{"id": "hard2_0099", "index": 99, "difficulty": "hard", "equation1": "x = y * (x * ((z * y) * y))", "equation2": "x = ((y * z) * (z * z)) * x", "answer": true}
|
| 100 |
-
{"id": "hard2_0100", "index": 100, "difficulty": "hard", "equation1": "x = (x * ((x * y) * y)) * y", "equation2": "x * y = ((x * y) * y) * x", "answer": false}
|
| 101 |
-
{"id": "hard2_0101", "index": 101, "difficulty": "hard", "equation1": "x = y * ((y * x) * z)", "equation2": "x = x * (x * (y * y))", "answer": true}
|
| 102 |
-
{"id": "hard2_0102", "index": 102, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = ((y * (z * x)) * w) * x", "answer": false}
|
| 103 |
-
{"id": "hard2_0103", "index": 103, "difficulty": "hard", "equation1": "x * y = y * ((z * x) * w)", "equation2": "x * x = (x * (x * y)) * z", "answer": true}
|
| 104 |
-
{"id": "hard2_0104", "index": 104, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x * y = (y * (y * z)) * y", "answer": false}
|
| 105 |
-
{"id": "hard2_0105", "index": 105, "difficulty": "hard", "equation1": "x = y * ((y * (y * x)) * x)", "equation2": "x * (x * y) = y * (x * y)", "answer": false}
|
| 106 |
-
{"id": "hard2_0106", "index": 106, "difficulty": "hard", "equation1": "x = (((y * y) * y) * x) * z", "equation2": "x = ((y * (z * w)) * u) * v", "answer": true}
|
| 107 |
-
{"id": "hard2_0107", "index": 107, "difficulty": "hard", "equation1": "x = (y * (y * z)) * (x * x)", "equation2": "x = x * ((y * (x * y)) * x)", "answer": true}
|
| 108 |
-
{"id": "hard2_0108", "index": 108, "difficulty": "hard", "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * (y * z) = (w * u) * z", "answer": false}
|
| 109 |
-
{"id": "hard2_0109", "index": 109, "difficulty": "hard", "equation1": "x = (y * x) * (x * (y * z))", "equation2": "x * (y * y) = (x * y) * x", "answer": false}
|
| 110 |
-
{"id": "hard2_0110", "index": 110, "difficulty": "hard", "equation1": "x = y * (((z * x) * x) * x)", "equation2": "x = x * ((x * (x * y)) * x)", "answer": true}
|
| 111 |
-
{"id": "hard2_0111", "index": 111, "difficulty": "hard", "equation1": "x = (y * ((y * x) * z)) * w", "equation2": "x * x = (x * (y * y)) * x", "answer": true}
|
| 112 |
-
{"id": "hard2_0112", "index": 112, "difficulty": "hard", "equation1": "x = (((x * y) * y) * x) * y", "equation2": "x * x = x * ((y * z) * x)", "answer": false}
|
| 113 |
-
{"id": "hard2_0113", "index": 113, "difficulty": "hard", "equation1": "x = (y * (x * (z * z))) * z", "equation2": "x = x * ((x * (y * x)) * z)", "answer": true}
|
| 114 |
-
{"id": "hard2_0114", "index": 114, "difficulty": "hard", "equation1": "x = (y * (x * x)) * z", "equation2": "x = y * ((z * (z * y)) * w)", "answer": true}
|
| 115 |
-
{"id": "hard2_0115", "index": 115, "difficulty": "hard", "equation1": "x = ((y * (z * x)) * x) * w", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 116 |
-
{"id": "hard2_0116", "index": 116, "difficulty": "hard", "equation1": "x = y * ((x * (z * z)) * z)", "equation2": "x = x * (((x * y) * z) * w)", "answer": true}
|
| 117 |
-
{"id": "hard2_0117", "index": 117, "difficulty": "hard", "equation1": "x * y = y * (y * (x * z))", "equation2": "x * y = (z * (w * u)) * v", "answer": true}
|
| 118 |
-
{"id": "hard2_0118", "index": 118, "difficulty": "hard", "equation1": "x = (x * ((x * y) * y)) * y", "equation2": "x = (x * y) * (x * (y * z))", "answer": false}
|
| 119 |
-
{"id": "hard2_0119", "index": 119, "difficulty": "hard", "equation1": "x = y * (x * (y * (y * z)))", "equation2": "x = ((x * x) * y) * x", "answer": true}
|
| 120 |
-
{"id": "hard2_0120", "index": 120, "difficulty": "hard", "equation1": "x = ((y * (x * x)) * x) * z", "equation2": "x = x * (((y * y) * y) * x)", "answer": true}
|
| 121 |
-
{"id": "hard2_0121", "index": 121, "difficulty": "hard", "equation1": "x = y * (z * ((y * x) * y))", "equation2": "x = x * (((y * y) * x) * z)", "answer": true}
|
| 122 |
-
{"id": "hard2_0122", "index": 122, "difficulty": "hard", "equation1": "x = y * ((y * (y * x)) * x)", "equation2": "x = y * (((z * x) * x) * x)", "answer": false}
|
| 123 |
-
{"id": "hard2_0123", "index": 123, "difficulty": "hard", "equation1": "x = y * (((z * y) * x) * z)", "equation2": "x * (y * z) = x * (z * y)", "answer": false}
|
| 124 |
-
{"id": "hard2_0124", "index": 124, "difficulty": "hard", "equation1": "x = ((x * x) * y) * (y * z)", "equation2": "x * x = x * (x * (y * z))", "answer": false}
|
| 125 |
-
{"id": "hard2_0125", "index": 125, "difficulty": "hard", "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x = ((x * x) * (y * y)) * x", "answer": false}
|
| 126 |
-
{"id": "hard2_0126", "index": 126, "difficulty": "hard", "equation1": "x = ((y * (z * x)) * w) * x", "equation2": "x * x = y * (x * x)", "answer": true}
|
| 127 |
-
{"id": "hard2_0127", "index": 127, "difficulty": "hard", "equation1": "x = y * (((x * x) * x) * z)", "equation2": "x = x * ((y * z) * (y * z))", "answer": true}
|
| 128 |
-
{"id": "hard2_0128", "index": 128, "difficulty": "hard", "equation1": "x = ((y * (y * x)) * z) * y", "equation2": "x = x * ((y * (z * z)) * y)", "answer": true}
|
| 129 |
-
{"id": "hard2_0129", "index": 129, "difficulty": "hard", "equation1": "x = y * (z * ((z * y) * x))", "equation2": "x = y * (x * ((y * x) * x))", "answer": false}
|
| 130 |
-
{"id": "hard2_0130", "index": 130, "difficulty": "hard", "equation1": "x = (y * (x * (z * w))) * y", "equation2": "x = (((y * z) * x) * y) * x", "answer": true}
|
| 131 |
-
{"id": "hard2_0131", "index": 131, "difficulty": "hard", "equation1": "x = ((y * (z * z)) * x) * w", "equation2": "x = y * ((z * (x * y)) * z)", "answer": true}
|
| 132 |
-
{"id": "hard2_0132", "index": 132, "difficulty": "hard", "equation1": "x = y * ((z * (x * x)) * w)", "equation2": "x * y = z * ((x * w) * y)", "answer": true}
|
| 133 |
-
{"id": "hard2_0133", "index": 133, "difficulty": "hard", "equation1": "x = y * ((x * z) * (z * y))", "equation2": "x = y * ((z * x) * (y * z))", "answer": false}
|
| 134 |
-
{"id": "hard2_0134", "index": 134, "difficulty": "hard", "equation1": "x = (y * (y * x)) * (y * x)", "equation2": "x * y = ((z * y) * w) * y", "answer": false}
|
| 135 |
-
{"id": "hard2_0135", "index": 135, "difficulty": "hard", "equation1": "(x * y) * z = (y * w) * u", "equation2": "x * (y * x) = z * (y * x)", "answer": false}
|
| 136 |
-
{"id": "hard2_0136", "index": 136, "difficulty": "hard", "equation1": "x = ((y * (x * x)) * y) * z", "equation2": "x = y * (x * (z * (z * y)))", "answer": true}
|
| 137 |
-
{"id": "hard2_0137", "index": 137, "difficulty": "hard", "equation1": "x = ((y * x) * z) * (x * z)", "equation2": "x = y * (z * (x * (w * w)))", "answer": true}
|
| 138 |
-
{"id": "hard2_0138", "index": 138, "difficulty": "hard", "equation1": "x = y * ((y * (y * z)) * x)", "equation2": "x = y * (x * (z * (x * x)))", "answer": true}
|
| 139 |
-
{"id": "hard2_0139", "index": 139, "difficulty": "hard", "equation1": "x = (x * y) * ((z * w) * x)", "equation2": "x * y = ((x * z) * x) * y", "answer": false}
|
| 140 |
-
{"id": "hard2_0140", "index": 140, "difficulty": "hard", "equation1": "x = x * (y * (z * (w * z)))", "equation2": "x = (x * ((x * y) * y)) * x", "answer": true}
|
| 141 |
-
{"id": "hard2_0141", "index": 141, "difficulty": "hard", "equation1": "x = ((y * (z * x)) * z) * z", "equation2": "x = ((y * z) * (y * y)) * x", "answer": true}
|
| 142 |
-
{"id": "hard2_0142", "index": 142, "difficulty": "hard", "equation1": "x = ((y * x) * x) * y", "equation2": "x * (x * y) = z * (z * y)", "answer": false}
|
| 143 |
-
{"id": "hard2_0143", "index": 143, "difficulty": "hard", "equation1": "(x * x) * y = (z * w) * u", "equation2": "x * (x * y) = z * (x * z)", "answer": false}
|
| 144 |
-
{"id": "hard2_0144", "index": 144, "difficulty": "hard", "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = (y * z) * (y * x)", "answer": false}
|
| 145 |
-
{"id": "hard2_0145", "index": 145, "difficulty": "hard", "equation1": "x = (y * ((y * x) * z)) * w", "equation2": "x = (y * ((y * y) * x)) * y", "answer": true}
|
| 146 |
-
{"id": "hard2_0146", "index": 146, "difficulty": "hard", "equation1": "x * x = y * (z * (w * u))", "equation2": "x * (x * y) = y * (y * x)", "answer": false}
|
| 147 |
-
{"id": "hard2_0147", "index": 147, "difficulty": "hard", "equation1": "x = ((y * (x * x)) * z) * z", "equation2": "x = y * (((y * x) * x) * x)", "answer": true}
|
| 148 |
-
{"id": "hard2_0148", "index": 148, "difficulty": "hard", "equation1": "(x * y) * z = (z * w) * u", "equation2": "x * (y * z) = (y * z) * z", "answer": false}
|
| 149 |
-
{"id": "hard2_0149", "index": 149, "difficulty": "hard", "equation1": "x = (y * (x * (z * w))) * w", "equation2": "x = (((y * y) * z) * x) * x", "answer": true}
|
| 150 |
-
{"id": "hard2_0150", "index": 150, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x * y = z * (w * (x * z))", "answer": false}
|
| 151 |
-
{"id": "hard2_0151", "index": 151, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = (x * ((y * z) * w)) * y", "answer": false}
|
| 152 |
-
{"id": "hard2_0152", "index": 152, "difficulty": "hard", "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * x) = (y * z) * w", "answer": false}
|
| 153 |
-
{"id": "hard2_0153", "index": 153, "difficulty": "hard", "equation1": "x = y * (x * ((y * z) * z))", "equation2": "x = y * ((y * (y * y)) * x)", "answer": true}
|
| 154 |
-
{"id": "hard2_0154", "index": 154, "difficulty": "hard", "equation1": "x = ((y * (z * y)) * x) * w", "equation2": "x = x * (((y * y) * x) * z)", "answer": true}
|
| 155 |
-
{"id": "hard2_0155", "index": 155, "difficulty": "hard", "equation1": "x * y = ((z * y) * x) * x", "equation2": "x * x = (y * (x * x)) * z", "answer": true}
|
| 156 |
-
{"id": "hard2_0156", "index": 156, "difficulty": "hard", "equation1": "x = (((x * y) * x) * y) * y", "equation2": "x = (((x * y) * y) * y) * z", "answer": false}
|
| 157 |
-
{"id": "hard2_0157", "index": 157, "difficulty": "hard", "equation1": "x = (x * ((x * y) * y)) * y", "equation2": "x * y = ((x * z) * x) * w", "answer": false}
|
| 158 |
-
{"id": "hard2_0158", "index": 158, "difficulty": "hard", "equation1": "x * x = (y * (z * w)) * u", "equation2": "x * y = ((z * y) * x) * w", "answer": false}
|
| 159 |
-
{"id": "hard2_0159", "index": 159, "difficulty": "hard", "equation1": "x = (y * ((x * x) * z)) * y", "equation2": "x = (((y * x) * z) * y) * y", "answer": true}
|
| 160 |
-
{"id": "hard2_0160", "index": 160, "difficulty": "hard", "equation1": "x = y * ((x * y) * (z * z))", "equation2": "x = (y * ((x * x) * x)) * y", "answer": true}
|
| 161 |
-
{"id": "hard2_0161", "index": 161, "difficulty": "hard", "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * x) = x * (y * x)", "answer": false}
|
| 162 |
-
{"id": "hard2_0162", "index": 162, "difficulty": "hard", "equation1": "x = (y * (x * (x * z))) * y", "equation2": "x = (((x * y) * z) * y) * x", "answer": true}
|
| 163 |
-
{"id": "hard2_0163", "index": 163, "difficulty": "hard", "equation1": "x = (x * (y * z)) * (w * x)", "equation2": "(x * y) * z = (x * w) * z", "answer": false}
|
| 164 |
-
{"id": "hard2_0164", "index": 164, "difficulty": "hard", "equation1": "x = y * ((z * x) * (z * z))", "equation2": "x = ((y * (z * y)) * y) * x", "answer": true}
|
| 165 |
-
{"id": "hard2_0165", "index": 165, "difficulty": "hard", "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = y * (x * ((z * y) * z))", "answer": false}
|
| 166 |
-
{"id": "hard2_0166", "index": 166, "difficulty": "hard", "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = ((x * z) * w) * x", "answer": false}
|
| 167 |
-
{"id": "hard2_0167", "index": 167, "difficulty": "hard", "equation1": "x = (x * ((y * x) * y)) * y", "equation2": "x * y = x * ((y * x) * z)", "answer": false}
|
| 168 |
-
{"id": "hard2_0168", "index": 168, "difficulty": "hard", "equation1": "x * y = y * (z * (y * x))", "equation2": "x * (y * y) = (y * z) * x", "answer": true}
|
| 169 |
-
{"id": "hard2_0169", "index": 169, "difficulty": "hard", "equation1": "x = (y * (y * (x * y))) * y", "equation2": "x = (x * ((x * x) * x)) * x", "answer": false}
|
| 170 |
-
{"id": "hard2_0170", "index": 170, "difficulty": "hard", "equation1": "x * y = (y * (x * z)) * w", "equation2": "x * x = (y * (z * y)) * z", "answer": true}
|
| 171 |
-
{"id": "hard2_0171", "index": 171, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x * y = (x * (z * z)) * w", "answer": false}
|
| 172 |
-
{"id": "hard2_0172", "index": 172, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = ((y * y) * z) * (z * x)", "answer": false}
|
| 173 |
-
{"id": "hard2_0173", "index": 173, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x * y = y * (z * (x * z))", "answer": false}
|
| 174 |
-
{"id": "hard2_0174", "index": 174, "difficulty": "hard", "equation1": "x = ((y * (x * x)) * z) * z", "equation2": "x = ((y * (y * z)) * w) * x", "answer": true}
|
| 175 |
-
{"id": "hard2_0175", "index": 175, "difficulty": "hard", "equation1": "x = ((y * z) * (z * x)) * y", "equation2": "x = ((x * (x * y)) * x) * y", "answer": false}
|
| 176 |
-
{"id": "hard2_0176", "index": 176, "difficulty": "hard", "equation1": "x = ((x * (y * y)) * z) * x", "equation2": "x = ((x * (y * z)) * w) * x", "answer": false}
|
| 177 |
-
{"id": "hard2_0177", "index": 177, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = (y * (x * (z * y))) * x", "answer": false}
|
| 178 |
-
{"id": "hard2_0178", "index": 178, "difficulty": "hard", "equation1": "x = x * ((y * z) * (x * y))", "equation2": "x = x * ((y * y) * (z * y))", "answer": true}
|
| 179 |
-
{"id": "hard2_0179", "index": 179, "difficulty": "hard", "equation1": "x = (y * x) * (x * (z * y))", "equation2": "(x * y) * x = (y * x) * x", "answer": false}
|
| 180 |
-
{"id": "hard2_0180", "index": 180, "difficulty": "hard", "equation1": "x * x = (y * (z * w)) * u", "equation2": "x * (y * z) = (z * x) * y", "answer": false}
|
| 181 |
-
{"id": "hard2_0181", "index": 181, "difficulty": "hard", "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x = ((x * (x * y)) * z) * x", "answer": false}
|
| 182 |
-
{"id": "hard2_0182", "index": 182, "difficulty": "hard", "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x * y = z * (y * (z * w))", "answer": false}
|
| 183 |
-
{"id": "hard2_0183", "index": 183, "difficulty": "hard", "equation1": "(x * y) * z = (x * w) * u", "equation2": "x * (x * y) = x * (x * z)", "answer": false}
|
| 184 |
-
{"id": "hard2_0184", "index": 184, "difficulty": "hard", "equation1": "x = (((y * z) * y) * w) * x", "equation2": "x = (x * ((y * y) * y)) * x", "answer": true}
|
| 185 |
-
{"id": "hard2_0185", "index": 185, "difficulty": "hard", "equation1": "x = y * (z * ((x * x) * z))", "equation2": "x = y * (((y * x) * x) * x)", "answer": true}
|
| 186 |
-
{"id": "hard2_0186", "index": 186, "difficulty": "hard", "equation1": "x = y * (x * ((x * x) * z))", "equation2": "x = y * (y * (x * (x * z)))", "answer": true}
|
| 187 |
-
{"id": "hard2_0187", "index": 187, "difficulty": "hard", "equation1": "x = (y * z) * (z * x)", "equation2": "x = y * ((y * (z * y)) * x)", "answer": false}
|
| 188 |
-
{"id": "hard2_0188", "index": 188, "difficulty": "hard", "equation1": "(x * y) * z = (z * w) * x", "equation2": "(x * x) * y = (z * w) * y", "answer": false}
|
| 189 |
-
{"id": "hard2_0189", "index": 189, "difficulty": "hard", "equation1": "x = (y * (y * (x * x))) * z", "equation2": "x * (y * x) = z * (x * w)", "answer": true}
|
| 190 |
-
{"id": "hard2_0190", "index": 190, "difficulty": "hard", "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = (z * w) * (y * y)", "answer": false}
|
| 191 |
-
{"id": "hard2_0191", "index": 191, "difficulty": "hard", "equation1": "x = (x * y) * ((x * y) * y)", "equation2": "x = (x * (x * y)) * z", "answer": false}
|
| 192 |
-
{"id": "hard2_0192", "index": 192, "difficulty": "hard", "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x * (x * y) = x * (z * x)", "answer": false}
|
| 193 |
-
{"id": "hard2_0193", "index": 193, "difficulty": "hard", "equation1": "x = ((y * z) * y) * (w * x)", "equation2": "x * (y * x) = y * (x * x)", "answer": true}
|
| 194 |
-
{"id": "hard2_0194", "index": 194, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = (y * (x * (y * x))) * y", "answer": false}
|
| 195 |
-
{"id": "hard2_0195", "index": 195, "difficulty": "hard", "equation1": "x * (x * y) = (z * y) * w", "equation2": "x * (y * x) = (z * z) * x", "answer": false}
|
| 196 |
-
{"id": "hard2_0196", "index": 196, "difficulty": "hard", "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = x * ((y * y) * (z * y))", "answer": false}
|
| 197 |
-
{"id": "hard2_0197", "index": 197, "difficulty": "hard", "equation1": "x * x = y * (z * (y * w))", "equation2": "x * x = y * (z * (x * z))", "answer": false}
|
| 198 |
-
{"id": "hard2_0198", "index": 198, "difficulty": "hard", "equation1": "x * y = z * (y * (x * x))", "equation2": "x * y = (z * w) * (z * x)", "answer": true}
|
| 199 |
-
{"id": "hard2_0199", "index": 199, "difficulty": "hard", "equation1": "x = ((x * y) * (x * z)) * w", "equation2": "x = ((x * (x * x)) * x) * y", "answer": true}
|
| 200 |
-
{"id": "hard2_0200", "index": 200, "difficulty": "hard", "equation1": "x * y = y * (z * (x * w))", "equation2": "x * y = (y * (z * w)) * u", "answer": true}
|
|
|
|
| 1 |
+
{"id": "hard2_0001", "index": 1, "difficulty": "hard", "eq1_id": 4538, "eq2_id": 4505, "equation1": "x * (y * z) = (y * w) * w", "equation2": "x * (y * y) = (z * w) * u", "answer": false}
|
| 2 |
+
{"id": "hard2_0002", "index": 2, "difficulty": "hard", "eq1_id": 1119, "eq2_id": 1979, "equation1": "x = y * ((y * (y * x)) * x)", "equation2": "x = (y * (z * y)) * (y * x)", "answer": false}
|
| 3 |
+
{"id": "hard2_0003", "index": 3, "difficulty": "hard", "eq1_id": 3348, "eq2_id": 3972, "equation1": "x * y = y * (x * (z * x))", "equation2": "x * y = (y * (z * x)) * y", "answer": true}
|
| 4 |
+
{"id": "hard2_0004", "index": 4, "difficulty": "hard", "eq1_id": 3141, "eq2_id": 1091, "equation1": "x = (((y * y) * x) * x) * z", "equation2": "x = y * ((x * (y * z)) * w)", "answer": true}
|
| 5 |
+
{"id": "hard2_0005", "index": 5, "difficulty": "hard", "eq1_id": 1181, "eq2_id": 2449, "equation1": "x = y * ((z * (z * x)) * y)", "equation2": "x = (x * ((x * y) * y)) * x", "answer": true}
|
| 6 |
+
{"id": "hard2_0006", "index": 6, "difficulty": "hard", "eq1_id": 540, "eq2_id": 2128, "equation1": "x = y * (z * (x * (x * w)))", "equation2": "x = ((y * y) * x) * (y * y)", "answer": true}
|
| 7 |
+
{"id": "hard2_0007", "index": 7, "difficulty": "hard", "eq1_id": 4422, "eq2_id": 4296, "equation1": "x * (x * y) = (z * y) * w", "equation2": "x * (x * y) = y * (z * y)", "answer": false}
|
| 8 |
+
{"id": "hard2_0008", "index": 8, "difficulty": "hard", "eq1_id": 470, "eq2_id": 622, "equation1": "x = y * (x * (x * (z * y)))", "equation2": "x = x * (x * ((y * y) * x))", "answer": true}
|
| 9 |
+
{"id": "hard2_0009", "index": 9, "difficulty": "hard", "eq1_id": 898, "eq2_id": 2673, "equation1": "x = y * ((x * z) * (z * y))", "equation2": "x = ((x * y) * (y * y)) * y", "answer": false}
|
| 10 |
+
{"id": "hard2_0010", "index": 10, "difficulty": "hard", "eq1_id": 1648, "eq2_id": 2239, "equation1": "x = (x * y) * ((x * y) * y)", "equation2": "x = (x * (x * (x * x))) * y", "answer": false}
|
| 11 |
+
{"id": "hard2_0011", "index": 11, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 249, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = (y * (z * z)) * w", "answer": false}
|
| 12 |
+
{"id": "hard2_0012", "index": 12, "difficulty": "hard", "eq1_id": 1368, "eq2_id": 4612, "equation1": "x = y * (((z * y) * x) * z)", "equation2": "(x * x) * y = (y * z) * z", "answer": false}
|
| 13 |
+
{"id": "hard2_0013", "index": 13, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 1230, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = x * (((x * y) * x) * z)", "answer": false}
|
| 14 |
+
{"id": "hard2_0014", "index": 14, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 4684, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "(x * y) * z = (z * y) * x", "answer": false}
|
| 15 |
+
{"id": "hard2_0015", "index": 15, "difficulty": "hard", "eq1_id": 3913, "eq2_id": 3820, "equation1": "x * x = (y * (z * w)) * u", "equation2": "x * y = (z * z) * (x * y)", "answer": false}
|
| 16 |
+
{"id": "hard2_0016", "index": 16, "difficulty": "hard", "eq1_id": 646, "eq2_id": 4127, "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x * y = ((x * y) * x) * x", "answer": false}
|
| 17 |
+
{"id": "hard2_0017", "index": 17, "difficulty": "hard", "eq1_id": 478, "eq2_id": 3034, "equation1": "x = y * (x * (y * (y * z)))", "equation2": "x = ((y * (z * w)) * z) * x", "answer": true}
|
| 18 |
+
{"id": "hard2_0018", "index": 18, "difficulty": "hard", "eq1_id": 1033, "eq2_id": 49, "equation1": "x = x * ((x * (y * z)) * z)", "equation2": "x = x * (x * (y * x))", "answer": true}
|
| 19 |
+
{"id": "hard2_0019", "index": 19, "difficulty": "hard", "eq1_id": 3162, "eq2_id": 4158, "equation1": "x = (((y * y) * z) * x) * w", "equation2": "x * y = ((y * x) * y) * y", "answer": true}
|
| 20 |
+
{"id": "hard2_0020", "index": 20, "difficulty": "hard", "eq1_id": 4373, "eq2_id": 4655, "equation1": "x * (y * z) = z * (w * u)", "equation2": "(x * y) * y = (x * z) * y", "answer": false}
|
| 21 |
+
{"id": "hard2_0021", "index": 21, "difficulty": "hard", "eq1_id": 3577, "eq2_id": 4618, "equation1": "x * y = y * ((z * w) * x)", "equation2": "(x * x) * y = (z * y) * x", "answer": true}
|
| 22 |
+
{"id": "hard2_0022", "index": 22, "difficulty": "hard", "eq1_id": 1294, "eq2_id": 2496, "equation1": "x = y * (((x * y) * z) * w)", "equation2": "x = (y * ((x * x) * y)) * x", "answer": true}
|
| 23 |
+
{"id": "hard2_0023", "index": 23, "difficulty": "hard", "eq1_id": 54, "eq2_id": 2488, "equation1": "x = x * (y * (x * z))", "equation2": "x = (x * ((y * z) * w)) * x", "answer": true}
|
| 24 |
+
{"id": "hard2_0024", "index": 24, "difficulty": "hard", "eq1_id": 82, "eq2_id": 709, "equation1": "x = y * (z * (x * x))", "equation2": "x = y * (y * ((x * z) * x))", "answer": true}
|
| 25 |
+
{"id": "hard2_0025", "index": 25, "difficulty": "hard", "eq1_id": 3532, "eq2_id": 3309, "equation1": "x * y = x * ((z * y) * x)", "equation2": "x * y = x * (x * (y * y))", "answer": false}
|
| 26 |
+
{"id": "hard2_0026", "index": 26, "difficulty": "hard", "eq1_id": 3126, "eq2_id": 2652, "equation1": "x = (((y * x) * z) * y) * x", "equation2": "x = ((x * x) * (y * y)) * x", "answer": true}
|
| 27 |
+
{"id": "hard2_0027", "index": 27, "difficulty": "hard", "eq1_id": 1167, "eq2_id": 1763, "equation1": "x = y * ((z * (y * y)) * x)", "equation2": "x = (y * z) * ((x * z) * x)", "answer": false}
|
| 28 |
+
{"id": "hard2_0028", "index": 28, "difficulty": "hard", "eq1_id": 3561, "eq2_id": 4195, "equation1": "x * y = y * ((y * z) * x)", "equation2": "x * y = ((z * x) * y) * x", "answer": true}
|
| 29 |
+
{"id": "hard2_0029", "index": 29, "difficulty": "hard", "eq1_id": 4164, "eq2_id": 3927, "equation1": "x * y = ((y * y) * x) * x", "equation2": "x * y = (x * (y * y)) * x", "answer": false}
|
| 30 |
+
{"id": "hard2_0030", "index": 30, "difficulty": "hard", "eq1_id": 697, "eq2_id": 4158, "equation1": "x = y * (x * ((z * z) * w))", "equation2": "x * y = ((y * x) * y) * y", "answer": true}
|
| 31 |
+
{"id": "hard2_0031", "index": 31, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 3046, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = ((y * (z * w)) * u) * z", "answer": false}
|
| 32 |
+
{"id": "hard2_0032", "index": 32, "difficulty": "hard", "eq1_id": 4001, "eq2_id": 3890, "equation1": "x * y = (z * (x * w)) * y", "equation2": "x * x = (y * (y * y)) * x", "answer": false}
|
| 33 |
+
{"id": "hard2_0033", "index": 33, "difficulty": "hard", "eq1_id": 1147, "eq2_id": 2511, "equation1": "x = y * ((z * (x * x)) * y)", "equation2": "x = (y * ((x * y) * z)) * z", "answer": true}
|
| 34 |
+
{"id": "hard2_0034", "index": 34, "difficulty": "hard", "eq1_id": 3959, "eq2_id": 3573, "equation1": "x * y = (y * (x * z)) * z", "equation2": "x * y = y * ((z * z) * x)", "answer": false}
|
| 35 |
+
{"id": "hard2_0035", "index": 35, "difficulty": "hard", "eq1_id": 2705, "eq2_id": 2306, "equation1": "x = ((y * x) * (x * z)) * w", "equation2": "x = (y * (x * (y * z))) * x", "answer": true}
|
| 36 |
+
{"id": "hard2_0036", "index": 36, "difficulty": "hard", "eq1_id": 1961, "eq2_id": 3155, "equation1": "x = (y * (z * x)) * (x * w)", "equation2": "x = (((y * y) * y) * z) * x", "answer": true}
|
| 37 |
+
{"id": "hard2_0037", "index": 37, "difficulty": "hard", "eq1_id": 3242, "eq2_id": 1251, "equation1": "x = (((y * z) * w) * w) * x", "equation2": "x = x * (((y * y) * y) * x)", "answer": true}
|
| 38 |
+
{"id": "hard2_0038", "index": 38, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 519, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = y * (y * (y * (z * w)))", "answer": false}
|
| 39 |
+
{"id": "hard2_0039", "index": 39, "difficulty": "hard", "eq1_id": 1111, "eq2_id": 2891, "equation1": "x = y * ((y * (x * x)) * z)", "equation2": "x = ((x * (y * z)) * z) * y", "answer": true}
|
| 40 |
+
{"id": "hard2_0040", "index": 40, "difficulty": "hard", "eq1_id": 685, "eq2_id": 49, "equation1": "x = y * (x * ((y * z) * w))", "equation2": "x = x * (x * (y * x))", "answer": true}
|
| 41 |
+
{"id": "hard2_0041", "index": 41, "difficulty": "hard", "eq1_id": 1112, "eq2_id": 1847, "equation1": "x = y * ((y * (x * y)) * x)", "equation2": "x = (x * (y * x)) * (x * x)", "answer": false}
|
| 42 |
+
{"id": "hard2_0042", "index": 42, "difficulty": "hard", "eq1_id": 4468, "eq2_id": 4560, "equation1": "x * (y * x) = (z * w) * u", "equation2": "x * (y * z) = (w * x) * w", "answer": false}
|
| 43 |
+
{"id": "hard2_0043", "index": 43, "difficulty": "hard", "eq1_id": 2856, "eq2_id": 4315, "equation1": "x = ((x * (x * y)) * y) * y", "equation2": "x * (y * x) = x * (y * z)", "answer": false}
|
| 44 |
+
{"id": "hard2_0044", "index": 44, "difficulty": "hard", "eq1_id": 2604, "eq2_id": 2677, "equation1": "x = (y * ((z * z) * x)) * w", "equation2": "x = ((x * y) * (y * z)) * z", "answer": true}
|
| 45 |
+
{"id": "hard2_0045", "index": 45, "difficulty": "hard", "eq1_id": 4116, "eq2_id": 3515, "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = x * ((x * z) * y)", "answer": false}
|
| 46 |
+
{"id": "hard2_0046", "index": 46, "difficulty": "hard", "eq1_id": 4692, "eq2_id": 4281, "equation1": "(x * y) * z = (w * z) * u", "equation2": "x * (x * x) = y * (z * w)", "answer": false}
|
| 47 |
+
{"id": "hard2_0047", "index": 47, "difficulty": "hard", "eq1_id": 3958, "eq2_id": 4067, "equation1": "x * y = (y * (x * z)) * y", "equation2": "x * x = ((x * x) * y) * x", "answer": false}
|
| 48 |
+
{"id": "hard2_0048", "index": 48, "difficulty": "hard", "eq1_id": 4690, "eq2_id": 4299, "equation1": "(x * y) * z = (w * y) * u", "equation2": "x * (x * y) = z * (x * x)", "answer": false}
|
| 49 |
+
{"id": "hard2_0049", "index": 49, "difficulty": "hard", "eq1_id": 1401, "eq2_id": 629, "equation1": "x = y * (((z * w) * x) * y)", "equation2": "x = x * (y * ((x * x) * x))", "answer": true}
|
| 50 |
+
{"id": "hard2_0050", "index": 50, "difficulty": "hard", "eq1_id": 136, "eq2_id": 3019, "equation1": "x = y * ((z * x) * z)", "equation2": "x = ((y * (z * z)) * w) * x", "answer": true}
|
| 51 |
+
{"id": "hard2_0051", "index": 51, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 4307, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x * (x * y) = z * (z * y)", "answer": false}
|
| 52 |
+
{"id": "hard2_0052", "index": 52, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 459, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = x * (y * (z * (w * y)))", "answer": false}
|
| 53 |
+
{"id": "hard2_0053", "index": 53, "difficulty": "hard", "eq1_id": 485, "eq2_id": 2128, "equation1": "x = y * (x * (z * (x * z)))", "equation2": "x = ((y * y) * x) * (y * y)", "answer": true}
|
| 54 |
+
{"id": "hard2_0054", "index": 54, "difficulty": "hard", "eq1_id": 4683, "eq2_id": 4495, "equation1": "(x * y) * z = (y * w) * u", "equation2": "x * (y * y) = (z * y) * z", "answer": false}
|
| 55 |
+
{"id": "hard2_0055", "index": 55, "difficulty": "hard", "eq1_id": 4468, "eq2_id": 4295, "equation1": "x * (y * x) = (z * w) * u", "equation2": "x * (x * y) = y * (z * x)", "answer": false}
|
| 56 |
+
{"id": "hard2_0056", "index": 56, "difficulty": "hard", "eq1_id": 1119, "eq2_id": 2207, "equation1": "x = y * ((y * (y * x)) * x)", "equation2": "x = ((y * z) * z) * (w * x)", "answer": false}
|
| 57 |
+
{"id": "hard2_0057", "index": 57, "difficulty": "hard", "eq1_id": 1212, "eq2_id": 2182, "equation1": "x = y * ((z * (w * w)) * x)", "equation2": "x = ((y * z) * y) * (y * x)", "answer": true}
|
| 58 |
+
{"id": "hard2_0058", "index": 58, "difficulty": "hard", "eq1_id": 1807, "eq2_id": 2385, "equation1": "x = (y * z) * ((w * x) * y)", "equation2": "x = (y * (z * (y * y))) * x", "answer": true}
|
| 59 |
+
{"id": "hard2_0059", "index": 59, "difficulty": "hard", "eq1_id": 1501, "eq2_id": 1073, "equation1": "x = (y * x) * (z * (x * w))", "equation2": "x = y * ((x * (x * x)) * y)", "answer": true}
|
| 60 |
+
{"id": "hard2_0060", "index": 60, "difficulty": "hard", "eq1_id": 636, "eq2_id": 1070, "equation1": "x = x * (y * ((x * z) * y))", "equation2": "x = x * ((y * (z * w)) * w)", "answer": true}
|
| 61 |
+
{"id": "hard2_0061", "index": 61, "difficulty": "hard", "eq1_id": 1283, "eq2_id": 722, "equation1": "x = y * (((x * x) * z) * z)", "equation2": "x = y * (y * ((y * z) * w))", "answer": true}
|
| 62 |
+
{"id": "hard2_0062", "index": 62, "difficulty": "hard", "eq1_id": 4116, "eq2_id": 4267, "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = ((z * w) * u) * v", "answer": false}
|
| 63 |
+
{"id": "hard2_0063", "index": 63, "difficulty": "hard", "eq1_id": 84, "eq2_id": 680, "equation1": "x = y * (z * (x * z))", "equation2": "x = y * (x * ((y * y) * y))", "answer": true}
|
| 64 |
+
{"id": "hard2_0064", "index": 64, "difficulty": "hard", "eq1_id": 1587, "eq2_id": 562, "equation1": "x = (y * z) * (z * (x * y))", "equation2": "x = y * (z * (y * (z * x)))", "answer": false}
|
| 65 |
+
{"id": "hard2_0065", "index": 65, "difficulty": "hard", "eq1_id": 3396, "eq2_id": 3928, "equation1": "x * y = z * (y * (x * x))", "equation2": "x * y = (x * (y * y)) * y", "answer": true}
|
| 66 |
+
{"id": "hard2_0066", "index": 66, "difficulty": "hard", "eq1_id": 1716, "eq2_id": 2469, "equation1": "x = (y * x) * ((z * w) * w)", "equation2": "x = (x * ((y * y) * y)) * x", "answer": true}
|
| 67 |
+
{"id": "hard2_0067", "index": 67, "difficulty": "hard", "eq1_id": 2116, "eq2_id": 1932, "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = (y * (y * y)) * (x * y)", "answer": false}
|
| 68 |
+
{"id": "hard2_0068", "index": 68, "difficulty": "hard", "eq1_id": 4431, "eq2_id": 4362, "equation1": "x * (x * y) = (z * w) * u", "equation2": "x * (y * z) = y * (x * z)", "answer": false}
|
| 69 |
+
{"id": "hard2_0069", "index": 69, "difficulty": "hard", "eq1_id": 1317, "eq2_id": 1021, "equation1": "x = y * (((y * x) * y) * z)", "equation2": "x = x * ((x * (x * x)) * y)", "answer": true}
|
| 70 |
+
{"id": "hard2_0070", "index": 70, "difficulty": "hard", "eq1_id": 3358, "eq2_id": 3944, "equation1": "x * y = y * (y * (z * x))", "equation2": "x * y = (x * (z * z)) * z", "answer": true}
|
| 71 |
+
{"id": "hard2_0071", "index": 71, "difficulty": "hard", "eq1_id": 4116, "eq2_id": 3408, "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = z * (y * (w * x))", "answer": false}
|
| 72 |
+
{"id": "hard2_0072", "index": 72, "difficulty": "hard", "eq1_id": 2908, "eq2_id": 1198, "equation1": "x = ((y * (x * x)) * z) * w", "equation2": "x = y * ((z * (w * x)) * y)", "answer": true}
|
| 73 |
+
{"id": "hard2_0073", "index": 73, "difficulty": "hard", "eq1_id": 2920, "eq2_id": 1248, "equation1": "x = ((y * (x * z)) * x) * y", "equation2": "x = x * (((y * y) * x) * x)", "answer": true}
|
| 74 |
+
{"id": "hard2_0074", "index": 74, "difficulty": "hard", "eq1_id": 1603, "eq2_id": 782, "equation1": "x = (y * z) * (w * (x * x))", "equation2": "x = y * (z * ((z * z) * x))", "answer": true}
|
| 75 |
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{"id": "hard2_0075", "index": 75, "difficulty": "hard", "eq1_id": 3010, "eq2_id": 2349, "equation1": "x = ((y * (z * z)) * x) * w", "equation2": "x = (y * (y * (z * x))) * z", "answer": true}
|
| 76 |
+
{"id": "hard2_0076", "index": 76, "difficulty": "hard", "eq1_id": 4653, "eq2_id": 4429, "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * y) = (z * w) * z", "answer": false}
|
| 77 |
+
{"id": "hard2_0077", "index": 77, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 3065, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = (((x * y) * x) * x) * x", "answer": false}
|
| 78 |
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{"id": "hard2_0078", "index": 78, "difficulty": "hard", "eq1_id": 3550, "eq2_id": 4088, "equation1": "x * y = y * ((x * y) * z)", "equation2": "x * x = ((y * x) * z) * z", "answer": true}
|
| 79 |
+
{"id": "hard2_0079", "index": 79, "difficulty": "hard", "eq1_id": 2307, "eq2_id": 680, "equation1": "x = (y * (x * (y * z))) * y", "equation2": "x = y * (x * ((y * y) * y))", "answer": true}
|
| 80 |
+
{"id": "hard2_0080", "index": 80, "difficulty": "hard", "eq1_id": 2788, "eq2_id": 632, "equation1": "x = ((y * z) * (y * x)) * y", "equation2": "x = x * (y * ((x * y) * x))", "answer": true}
|
| 81 |
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{"id": "hard2_0081", "index": 81, "difficulty": "hard", "eq1_id": 2299, "eq2_id": 633, "equation1": "x = (y * (x * (x * z))) * w", "equation2": "x = x * (y * ((x * y) * y))", "answer": true}
|
| 82 |
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{"id": "hard2_0082", "index": 82, "difficulty": "hard", "eq1_id": 3577, "eq2_id": 3798, "equation1": "x * y = y * ((z * w) * x)", "equation2": "x * y = (z * x) * (w * y)", "answer": true}
|
| 83 |
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{"id": "hard2_0083", "index": 83, "difficulty": "hard", "eq1_id": 2178, "eq2_id": 3431, "equation1": "x = ((y * z) * y) * (x * x)", "equation2": "x * y = z * (w * (x * y))", "answer": true}
|
| 84 |
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{"id": "hard2_0084", "index": 84, "difficulty": "hard", "eq1_id": 4545, "eq2_id": 4534, "equation1": "x * (y * z) = (z * y) * y", "equation2": "x * (y * z) = (y * z) * w", "answer": false}
|
| 85 |
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{"id": "hard2_0085", "index": 85, "difficulty": "hard", "eq1_id": 2786, "eq2_id": 3105, "equation1": "x = ((y * z) * (x * w)) * u", "equation2": "x = (((y * x) * x) * y) * x", "answer": true}
|
| 86 |
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{"id": "hard2_0086", "index": 86, "difficulty": "hard", "eq1_id": 2604, "eq2_id": 1316, "equation1": "x = (y * ((z * z) * x)) * w", "equation2": "x = y * (((y * x) * y) * y)", "answer": true}
|
| 87 |
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{"id": "hard2_0087", "index": 87, "difficulty": "hard", "eq1_id": 4422, "eq2_id": 4297, "equation1": "x * (x * y) = (z * y) * w", "equation2": "x * (x * y) = y * (z * z)", "answer": false}
|
| 88 |
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{"id": "hard2_0088", "index": 88, "difficulty": "hard", "eq1_id": 206, "eq2_id": 4358, "equation1": "x = (x * (x * y)) * y", "equation2": "x * (y * z) = x * (z * y)", "answer": false}
|
| 89 |
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{"id": "hard2_0089", "index": 89, "difficulty": "hard", "eq1_id": 1284, "eq2_id": 2435, "equation1": "x = y * (((x * x) * z) * w)", "equation2": "x = (y * (z * (w * u))) * x", "answer": true}
|
| 90 |
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{"id": "hard2_0090", "index": 90, "difficulty": "hard", "eq1_id": 3958, "eq2_id": 4128, "equation1": "x * y = (y * (x * z)) * y", "equation2": "x * y = ((x * y) * x) * y", "answer": false}
|
| 91 |
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{"id": "hard2_0091", "index": 91, "difficulty": "hard", "eq1_id": 1298, "eq2_id": 2948, "equation1": "x = y * (((x * z) * x) * w)", "equation2": "x = ((y * (y * y)) * x) * z", "answer": true}
|
| 92 |
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{"id": "hard2_0092", "index": 92, "difficulty": "hard", "eq1_id": 4581, "eq2_id": 4539, "equation1": "x * (y * z) = (w * u) * u", "equation2": "x * (y * z) = (y * w) * u", "answer": false}
|
| 93 |
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{"id": "hard2_0093", "index": 93, "difficulty": "hard", "eq1_id": 1518, "eq2_id": 3915, "equation1": "x = (y * y) * (x * (y * x))", "equation2": "x * y = (x * (x * x)) * y", "answer": false}
|
| 94 |
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{"id": "hard2_0094", "index": 94, "difficulty": "hard", "eq1_id": 1074, "eq2_id": 2083, "equation1": "x = y * ((x * (x * x)) * z)", "equation2": "x = ((x * y) * z) * (w * y)", "answer": true}
|
| 95 |
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{"id": "hard2_0095", "index": 95, "difficulty": "hard", "eq1_id": 1184, "eq2_id": 3962, "equation1": "x = y * ((z * (z * y)) * x)", "equation2": "x * y = (y * (y * x)) * y", "answer": false}
|
| 96 |
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{"id": "hard2_0096", "index": 96, "difficulty": "hard", "eq1_id": 964, "eq2_id": 4192, "equation1": "x = y * ((z * y) * (y * x))", "equation2": "x * y = ((z * x) * x) * y", "answer": false}
|
| 97 |
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{"id": "hard2_0097", "index": 97, "difficulty": "hard", "eq1_id": 2248, "eq2_id": 4079, "equation1": "x = (x * (x * (y * y))) * z", "equation2": "x * x = ((x * y) * z) * w", "answer": true}
|
| 98 |
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{"id": "hard2_0098", "index": 98, "difficulty": "hard", "eq1_id": 2307, "eq2_id": 1109, "equation1": "x = (y * (x * (y * z))) * y", "equation2": "x = y * ((y * (x * x)) * x)", "answer": true}
|
| 99 |
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{"id": "hard2_0099", "index": 99, "difficulty": "hard", "eq1_id": 691, "eq2_id": 2812, "equation1": "x = y * (x * ((z * y) * y))", "equation2": "x = ((y * z) * (z * z)) * x", "answer": true}
|
| 100 |
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{"id": "hard2_0100", "index": 100, "difficulty": "hard", "eq1_id": 2450, "eq2_id": 4130, "equation1": "x = (x * ((x * y) * y)) * y", "equation2": "x * y = ((x * y) * y) * x", "answer": false}
|
| 101 |
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{"id": "hard2_0101", "index": 101, "difficulty": "hard", "eq1_id": 126, "eq2_id": 50, "equation1": "x = y * ((y * x) * z)", "equation2": "x = x * (x * (y * y))", "answer": true}
|
| 102 |
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{"id": "hard2_0102", "index": 102, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 2985, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = ((y * (z * x)) * w) * x", "answer": false}
|
| 103 |
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{"id": "hard2_0103", "index": 103, "difficulty": "hard", "eq1_id": 3568, "eq2_id": 3866, "equation1": "x * y = y * ((z * x) * w)", "equation2": "x * x = (x * (x * y)) * z", "answer": true}
|
| 104 |
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{"id": "hard2_0104", "index": 104, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 3968, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x * y = (y * (y * z)) * y", "answer": false}
|
| 105 |
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{"id": "hard2_0105", "index": 105, "difficulty": "hard", "eq1_id": 1119, "eq2_id": 4291, "equation1": "x = y * ((y * (y * x)) * x)", "equation2": "x * (x * y) = y * (x * y)", "answer": false}
|
| 106 |
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{"id": "hard2_0106", "index": 106, "difficulty": "hard", "eq1_id": 3151, "eq2_id": 3049, "equation1": "x = (((y * y) * y) * x) * z", "equation2": "x = ((y * (z * w)) * u) * v", "answer": true}
|
| 107 |
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{"id": "hard2_0107", "index": 107, "difficulty": "hard", "eq1_id": 1941, "eq2_id": 1038, "equation1": "x = (y * (y * z)) * (x * x)", "equation2": "x = x * ((y * (x * y)) * x)", "answer": true}
|
| 108 |
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{"id": "hard2_0108", "index": 108, "difficulty": "hard", "eq1_id": 4116, "eq2_id": 4579, "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * (y * z) = (w * u) * z", "answer": false}
|
| 109 |
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{"id": "hard2_0109", "index": 109, "difficulty": "hard", "eq1_id": 1483, "eq2_id": 4472, "equation1": "x = (y * x) * (x * (y * z))", "equation2": "x * (y * y) = (x * y) * x", "answer": false}
|
| 110 |
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{"id": "hard2_0110", "index": 110, "difficulty": "hard", "eq1_id": 1349, "eq2_id": 1022, "equation1": "x = y * (((z * x) * x) * x)", "equation2": "x = x * ((x * (x * y)) * x)", "answer": true}
|
| 111 |
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{"id": "hard2_0111", "index": 111, "difficulty": "hard", "eq1_id": 2539, "eq2_id": 3870, "equation1": "x = (y * ((y * x) * z)) * w", "equation2": "x * x = (x * (y * y)) * x", "answer": true}
|
| 112 |
+
{"id": "hard2_0112", "index": 112, "difficulty": "hard", "eq1_id": 3076, "eq2_id": 3467, "equation1": "x = (((x * y) * y) * x) * y", "equation2": "x * x = x * ((y * z) * x)", "answer": false}
|
| 113 |
+
{"id": "hard2_0113", "index": 113, "difficulty": "hard", "eq1_id": 2320, "eq2_id": 1027, "equation1": "x = (y * (x * (z * z))) * z", "equation2": "x = x * ((x * (y * x)) * z)", "answer": true}
|
| 114 |
+
{"id": "hard2_0114", "index": 114, "difficulty": "hard", "eq1_id": 220, "eq2_id": 1187, "equation1": "x = (y * (x * x)) * z", "equation2": "x = y * ((z * (z * y)) * w)", "answer": true}
|
| 115 |
+
{"id": "hard2_0115", "index": 115, "difficulty": "hard", "eq1_id": 2976, "eq2_id": 1045, "equation1": "x = ((y * (z * x)) * x) * w", "equation2": "x = x * ((y * (y * x)) * x)", "answer": true}
|
| 116 |
+
{"id": "hard2_0116", "index": 116, "difficulty": "hard", "eq1_id": 1102, "eq2_id": 1237, "equation1": "x = y * ((x * (z * z)) * z)", "equation2": "x = x * (((x * y) * z) * w)", "answer": true}
|
| 117 |
+
{"id": "hard2_0117", "index": 117, "difficulty": "hard", "eq1_id": 3354, "eq2_id": 4064, "equation1": "x * y = y * (y * (x * z))", "equation2": "x * y = (z * (w * u)) * v", "answer": true}
|
| 118 |
+
{"id": "hard2_0118", "index": 118, "difficulty": "hard", "eq1_id": 2450, "eq2_id": 1446, "equation1": "x = (x * ((x * y) * y)) * y", "equation2": "x = (x * y) * (x * (y * z))", "answer": false}
|
| 119 |
+
{"id": "hard2_0119", "index": 119, "difficulty": "hard", "eq1_id": 478, "eq2_id": 257, "equation1": "x = y * (x * (y * (y * z)))", "equation2": "x = ((x * x) * y) * x", "answer": true}
|
| 120 |
+
{"id": "hard2_0120", "index": 120, "difficulty": "hard", "eq1_id": 2901, "eq2_id": 1251, "equation1": "x = ((y * (x * x)) * x) * z", "equation2": "x = x * (((y * y) * y) * x)", "answer": true}
|
| 121 |
+
{"id": "hard2_0121", "index": 121, "difficulty": "hard", "eq1_id": 758, "eq2_id": 1250, "equation1": "x = y * (z * ((y * x) * y))", "equation2": "x = x * (((y * y) * x) * z)", "answer": true}
|
| 122 |
+
{"id": "hard2_0122", "index": 122, "difficulty": "hard", "eq1_id": 1119, "eq2_id": 1349, "equation1": "x = y * ((y * (y * x)) * x)", "equation2": "x = y * (((z * x) * x) * x)", "answer": false}
|
| 123 |
+
{"id": "hard2_0123", "index": 123, "difficulty": "hard", "eq1_id": 1368, "eq2_id": 4358, "equation1": "x = y * (((z * y) * x) * z)", "equation2": "x * (y * z) = x * (z * y)", "answer": false}
|
| 124 |
+
{"id": "hard2_0124", "index": 124, "difficulty": "hard", "eq1_id": 2045, "eq2_id": 3257, "equation1": "x = ((x * x) * y) * (y * z)", "equation2": "x * x = x * (x * (y * z))", "answer": false}
|
| 125 |
+
{"id": "hard2_0125", "index": 125, "difficulty": "hard", "eq1_id": 2890, "eq2_id": 2652, "equation1": "x = ((x * (y * z)) * z) * x", "equation2": "x = ((x * x) * (y * y)) * x", "answer": false}
|
| 126 |
+
{"id": "hard2_0126", "index": 126, "difficulty": "hard", "eq1_id": 2985, "eq2_id": 312, "equation1": "x = ((y * (z * x)) * w) * x", "equation2": "x * x = y * (x * x)", "answer": true}
|
| 127 |
+
{"id": "hard2_0127", "index": 127, "difficulty": "hard", "eq1_id": 1277, "eq2_id": 858, "equation1": "x = y * (((x * x) * x) * z)", "equation2": "x = x * ((y * z) * (y * z))", "answer": true}
|
| 128 |
+
{"id": "hard2_0128", "index": 128, "difficulty": "hard", "eq1_id": 2943, "eq2_id": 1064, "equation1": "x = ((y * (y * x)) * z) * y", "equation2": "x = x * ((y * (z * z)) * y)", "answer": true}
|
| 129 |
+
{"id": "hard2_0129", "index": 129, "difficulty": "hard", "eq1_id": 778, "eq2_id": 676, "equation1": "x = y * (z * ((z * y) * x))", "equation2": "x = y * (x * ((y * x) * x))", "answer": false}
|
| 130 |
+
{"id": "hard2_0130", "index": 130, "difficulty": "hard", "eq1_id": 2323, "eq2_id": 3180, "equation1": "x = (y * (x * (z * w))) * y", "equation2": "x = (((y * z) * x) * y) * x", "answer": true}
|
| 131 |
+
{"id": "hard2_0131", "index": 131, "difficulty": "hard", "eq1_id": 3010, "eq2_id": 1152, "equation1": "x = ((y * (z * z)) * x) * w", "equation2": "x = y * ((z * (x * y)) * z)", "answer": true}
|
| 132 |
+
{"id": "hard2_0132", "index": 132, "difficulty": "hard", "eq1_id": 1149, "eq2_id": 3595, "equation1": "x = y * ((z * (x * x)) * w)", "equation2": "x * y = z * ((x * w) * y)", "answer": true}
|
| 133 |
+
{"id": "hard2_0133", "index": 133, "difficulty": "hard", "eq1_id": 898, "eq2_id": 949, "equation1": "x = y * ((x * z) * (z * y))", "equation2": "x = y * ((z * x) * (y * z))", "answer": false}
|
| 134 |
+
{"id": "hard2_0134", "index": 134, "difficulty": "hard", "eq1_id": 1924, "eq2_id": 4221, "equation1": "x = (y * (y * x)) * (y * x)", "equation2": "x * y = ((z * y) * w) * y", "answer": false}
|
| 135 |
+
{"id": "hard2_0135", "index": 135, "difficulty": "hard", "eq1_id": 4683, "eq2_id": 4330, "equation1": "(x * y) * z = (y * w) * u", "equation2": "x * (y * x) = z * (y * x)", "answer": false}
|
| 136 |
+
{"id": "hard2_0136", "index": 136, "difficulty": "hard", "eq1_id": 2904, "eq2_id": 492, "equation1": "x = ((y * (x * x)) * y) * z", "equation2": "x = y * (x * (z * (z * y)))", "answer": true}
|
| 137 |
+
{"id": "hard2_0137", "index": 137, "difficulty": "hard", "eq1_id": 2109, "eq2_id": 552, "equation1": "x = ((y * x) * z) * (x * z)", "equation2": "x = y * (z * (x * (w * w)))", "answer": true}
|
| 138 |
+
{"id": "hard2_0138", "index": 138, "difficulty": "hard", "eq1_id": 1125, "eq2_id": 483, "equation1": "x = y * ((y * (y * z)) * x)", "equation2": "x = y * (x * (z * (x * x)))", "answer": true}
|
| 139 |
+
{"id": "hard2_0139", "index": 139, "difficulty": "hard", "eq1_id": 1676, "eq2_id": 4138, "equation1": "x = (x * y) * ((z * w) * x)", "equation2": "x * y = ((x * z) * x) * y", "answer": false}
|
| 140 |
+
{"id": "hard2_0140", "index": 140, "difficulty": "hard", "eq1_id": 460, "eq2_id": 2449, "equation1": "x = x * (y * (z * (w * z)))", "equation2": "x = (x * ((x * y) * y)) * x", "answer": true}
|
| 141 |
+
{"id": "hard2_0141", "index": 141, "difficulty": "hard", "eq1_id": 2983, "eq2_id": 2791, "equation1": "x = ((y * (z * x)) * z) * z", "equation2": "x = ((y * z) * (y * y)) * x", "answer": true}
|
| 142 |
+
{"id": "hard2_0142", "index": 142, "difficulty": "hard", "eq1_id": 271, "eq2_id": 4307, "equation1": "x = ((y * x) * x) * y", "equation2": "x * (x * y) = z * (z * y)", "answer": false}
|
| 143 |
+
{"id": "hard2_0143", "index": 143, "difficulty": "hard", "eq1_id": 4628, "eq2_id": 4301, "equation1": "(x * x) * y = (z * w) * u", "equation2": "x * (x * y) = z * (x * z)", "answer": false}
|
| 144 |
+
{"id": "hard2_0144", "index": 144, "difficulty": "hard", "eq1_id": 4116, "eq2_id": 3772, "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = (y * z) * (y * x)", "answer": false}
|
| 145 |
+
{"id": "hard2_0145", "index": 145, "difficulty": "hard", "eq1_id": 2539, "eq2_id": 2541, "equation1": "x = (y * ((y * x) * z)) * w", "equation2": "x = (y * ((y * y) * x)) * y", "answer": true}
|
| 146 |
+
{"id": "hard2_0146", "index": 146, "difficulty": "hard", "eq1_id": 3304, "eq2_id": 4293, "equation1": "x * x = y * (z * (w * u))", "equation2": "x * (x * y) = y * (y * x)", "answer": false}
|
| 147 |
+
{"id": "hard2_0147", "index": 147, "difficulty": "hard", "eq1_id": 2907, "eq2_id": 1312, "equation1": "x = ((y * (x * x)) * z) * z", "equation2": "x = y * (((y * x) * x) * x)", "answer": true}
|
| 148 |
+
{"id": "hard2_0148", "index": 148, "difficulty": "hard", "eq1_id": 4688, "eq2_id": 4533, "equation1": "(x * y) * z = (z * w) * u", "equation2": "x * (y * z) = (y * z) * z", "answer": false}
|
| 149 |
+
{"id": "hard2_0149", "index": 149, "difficulty": "hard", "eq1_id": 2325, "eq2_id": 3159, "equation1": "x = (y * (x * (z * w))) * w", "equation2": "x = (((y * y) * z) * x) * x", "answer": true}
|
| 150 |
+
{"id": "hard2_0150", "index": 150, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 3432, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x * y = z * (w * (x * z))", "answer": false}
|
| 151 |
+
{"id": "hard2_0151", "index": 151, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 2489, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = (x * ((y * z) * w)) * y", "answer": false}
|
| 152 |
+
{"id": "hard2_0152", "index": 152, "difficulty": "hard", "eq1_id": 4653, "eq2_id": 4394, "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * x) = (y * z) * w", "answer": false}
|
| 153 |
+
{"id": "hard2_0153", "index": 153, "difficulty": "hard", "eq1_id": 684, "eq2_id": 1122, "equation1": "x = y * (x * ((y * z) * z))", "equation2": "x = y * ((y * (y * y)) * x)", "answer": true}
|
| 154 |
+
{"id": "hard2_0154", "index": 154, "difficulty": "hard", "eq1_id": 2993, "eq2_id": 1250, "equation1": "x = ((y * (z * y)) * x) * w", "equation2": "x = x * (((y * y) * x) * z)", "answer": true}
|
| 155 |
+
{"id": "hard2_0155", "index": 155, "difficulty": "hard", "eq1_id": 4208, "eq2_id": 3879, "equation1": "x * y = ((z * y) * x) * x", "equation2": "x * x = (y * (x * x)) * z", "answer": true}
|
| 156 |
+
{"id": "hard2_0156", "index": 156, "difficulty": "hard", "eq1_id": 3069, "eq2_id": 3080, "equation1": "x = (((x * y) * x) * y) * y", "equation2": "x = (((x * y) * y) * y) * z", "answer": false}
|
| 157 |
+
{"id": "hard2_0157", "index": 157, "difficulty": "hard", "eq1_id": 2450, "eq2_id": 4140, "equation1": "x = (x * ((x * y) * y)) * y", "equation2": "x * y = ((x * z) * x) * w", "answer": false}
|
| 158 |
+
{"id": "hard2_0158", "index": 158, "difficulty": "hard", "eq1_id": 3913, "eq2_id": 4211, "equation1": "x * x = (y * (z * w)) * u", "equation2": "x * y = ((z * y) * x) * w", "answer": false}
|
| 159 |
+
{"id": "hard2_0159", "index": 159, "difficulty": "hard", "eq1_id": 2500, "eq2_id": 3127, "equation1": "x = (y * ((x * x) * z)) * y", "equation2": "x = (((y * x) * z) * y) * y", "answer": true}
|
| 160 |
+
{"id": "hard2_0160", "index": 160, "difficulty": "hard", "eq1_id": 887, "eq2_id": 2494, "equation1": "x = y * ((x * y) * (z * z))", "equation2": "x = (y * ((x * x) * x)) * y", "answer": true}
|
| 161 |
+
{"id": "hard2_0161", "index": 161, "difficulty": "hard", "eq1_id": 4653, "eq2_id": 4269, "equation1": "(x * y) * x = (z * w) * u", "equation2": "x * (x * x) = x * (y * x)", "answer": false}
|
| 162 |
+
{"id": "hard2_0162", "index": 162, "difficulty": "hard", "eq1_id": 2297, "eq2_id": 3089, "equation1": "x = (y * (x * (x * z))) * y", "equation2": "x = (((x * y) * z) * y) * x", "answer": true}
|
| 163 |
+
{"id": "hard2_0163", "index": 163, "difficulty": "hard", "eq1_id": 1879, "eq2_id": 4675, "equation1": "x = (x * (y * z)) * (w * x)", "equation2": "(x * y) * z = (x * w) * z", "answer": false}
|
| 164 |
+
{"id": "hard2_0164", "index": 164, "difficulty": "hard", "eq1_id": 953, "eq2_id": 2994, "equation1": "x = y * ((z * x) * (z * z))", "equation2": "x = ((y * (z * y)) * y) * x", "answer": true}
|
| 165 |
+
{"id": "hard2_0165", "index": 165, "difficulty": "hard", "eq1_id": 2116, "eq2_id": 692, "equation1": "x = ((y * x) * z) * (z * y)", "equation2": "x = y * (x * ((z * y) * z))", "answer": false}
|
| 166 |
+
{"id": "hard2_0166", "index": 166, "difficulty": "hard", "eq1_id": 4116, "eq2_id": 4149, "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = ((x * z) * w) * x", "answer": false}
|
| 167 |
+
{"id": "hard2_0167", "index": 167, "difficulty": "hard", "eq1_id": 2460, "eq2_id": 3520, "equation1": "x = (x * ((y * x) * y)) * y", "equation2": "x * y = x * ((y * x) * z)", "answer": false}
|
| 168 |
+
{"id": "hard2_0168", "index": 168, "difficulty": "hard", "eq1_id": 3366, "eq2_id": 4485, "equation1": "x * y = y * (z * (y * x))", "equation2": "x * (y * y) = (y * z) * x", "answer": true}
|
| 169 |
+
{"id": "hard2_0169", "index": 169, "difficulty": "hard", "eq1_id": 2331, "eq2_id": 2441, "equation1": "x = (y * (y * (x * y))) * y", "equation2": "x = (x * ((x * x) * x)) * x", "answer": false}
|
| 170 |
+
{"id": "hard2_0170", "index": 170, "difficulty": "hard", "eq1_id": 3960, "eq2_id": 3903, "equation1": "x * y = (y * (x * z)) * w", "equation2": "x * x = (y * (z * y)) * z", "answer": true}
|
| 171 |
+
{"id": "hard2_0171", "index": 171, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 3945, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x * y = (x * (z * z)) * w", "answer": false}
|
| 172 |
+
{"id": "hard2_0172", "index": 172, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 2152, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x = ((y * y) * z) * (z * x)", "answer": false}
|
| 173 |
+
{"id": "hard2_0173", "index": 173, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 3364, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x * y = y * (z * (x * z))", "answer": false}
|
| 174 |
+
{"id": "hard2_0174", "index": 174, "difficulty": "hard", "eq1_id": 2907, "eq2_id": 2968, "equation1": "x = ((y * (x * x)) * z) * z", "equation2": "x = ((y * (y * z)) * w) * x", "answer": true}
|
| 175 |
+
{"id": "hard2_0175", "index": 175, "difficulty": "hard", "eq1_id": 2805, "eq2_id": 2853, "equation1": "x = ((y * z) * (z * x)) * y", "equation2": "x = ((x * (x * y)) * x) * y", "answer": false}
|
| 176 |
+
{"id": "hard2_0176", "index": 176, "difficulty": "hard", "eq1_id": 2878, "eq2_id": 2894, "equation1": "x = ((x * (y * y)) * z) * x", "equation2": "x = ((x * (y * z)) * w) * x", "answer": false}
|
| 177 |
+
{"id": "hard2_0177", "index": 177, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 2314, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = (y * (x * (z * y))) * x", "answer": false}
|
| 178 |
+
{"id": "hard2_0178", "index": 178, "difficulty": "hard", "eq1_id": 853, "eq2_id": 849, "equation1": "x = x * ((y * z) * (x * y))", "equation2": "x = x * ((y * y) * (z * y))", "answer": true}
|
| 179 |
+
{"id": "hard2_0179", "index": 179, "difficulty": "hard", "eq1_id": 1485, "eq2_id": 4635, "equation1": "x = (y * x) * (x * (z * y))", "equation2": "(x * y) * x = (y * x) * x", "answer": false}
|
| 180 |
+
{"id": "hard2_0180", "index": 180, "difficulty": "hard", "eq1_id": 3913, "eq2_id": 4541, "equation1": "x * x = (y * (z * w)) * u", "equation2": "x * (y * z) = (z * x) * y", "answer": false}
|
| 181 |
+
{"id": "hard2_0181", "index": 181, "difficulty": "hard", "eq1_id": 646, "eq2_id": 2858, "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x = ((x * (x * y)) * z) * x", "answer": false}
|
| 182 |
+
{"id": "hard2_0182", "index": 182, "difficulty": "hard", "eq1_id": 1076, "eq2_id": 3407, "equation1": "x = y * ((x * (x * y)) * y)", "equation2": "x * y = z * (y * (z * w))", "answer": false}
|
| 183 |
+
{"id": "hard2_0183", "index": 183, "difficulty": "hard", "eq1_id": 4676, "eq2_id": 4282, "equation1": "(x * y) * z = (x * w) * u", "equation2": "x * (x * y) = x * (x * z)", "answer": false}
|
| 184 |
+
{"id": "hard2_0184", "index": 184, "difficulty": "hard", "eq1_id": 3205, "eq2_id": 2469, "equation1": "x = (((y * z) * y) * w) * x", "equation2": "x = (x * ((y * y) * y)) * x", "answer": true}
|
| 185 |
+
{"id": "hard2_0185", "index": 185, "difficulty": "hard", "eq1_id": 742, "eq2_id": 1312, "equation1": "x = y * (z * ((x * x) * z))", "equation2": "x = y * (((y * x) * x) * x)", "answer": true}
|
| 186 |
+
{"id": "hard2_0186", "index": 186, "difficulty": "hard", "eq1_id": 668, "eq2_id": 502, "equation1": "x = y * (x * ((x * x) * z))", "equation2": "x = y * (y * (x * (x * z)))", "answer": true}
|
| 187 |
+
{"id": "hard2_0187", "index": 187, "difficulty": "hard", "eq1_id": 194, "eq2_id": 1133, "equation1": "x = (y * z) * (z * x)", "equation2": "x = y * ((y * (z * y)) * x)", "answer": false}
|
| 188 |
+
{"id": "hard2_0188", "index": 188, "difficulty": "hard", "eq1_id": 4686, "eq2_id": 4625, "equation1": "(x * y) * z = (z * w) * x", "equation2": "(x * x) * y = (z * w) * y", "answer": false}
|
| 189 |
+
{"id": "hard2_0189", "index": 189, "difficulty": "hard", "eq1_id": 2329, "eq2_id": 4329, "equation1": "x = (y * (y * (x * x))) * z", "equation2": "x * (y * x) = z * (x * w)", "answer": true}
|
| 190 |
+
{"id": "hard2_0190", "index": 190, "difficulty": "hard", "eq1_id": 4116, "eq2_id": 3842, "equation1": "x * x = ((y * z) * w) * u", "equation2": "x * y = (z * w) * (y * y)", "answer": false}
|
| 191 |
+
{"id": "hard2_0191", "index": 191, "difficulty": "hard", "eq1_id": 1648, "eq2_id": 207, "equation1": "x = (x * y) * ((x * y) * y)", "equation2": "x = (x * (x * y)) * z", "answer": false}
|
| 192 |
+
{"id": "hard2_0192", "index": 192, "difficulty": "hard", "eq1_id": 646, "eq2_id": 4286, "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x * (x * y) = x * (z * x)", "answer": false}
|
| 193 |
+
{"id": "hard2_0193", "index": 193, "difficulty": "hard", "eq1_id": 2190, "eq2_id": 4320, "equation1": "x = ((y * z) * y) * (w * x)", "equation2": "x * (y * x) = y * (x * x)", "answer": true}
|
| 194 |
+
{"id": "hard2_0194", "index": 194, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 2301, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = (y * (x * (y * x))) * y", "answer": false}
|
| 195 |
+
{"id": "hard2_0195", "index": 195, "difficulty": "hard", "eq1_id": 4422, "eq2_id": 4460, "equation1": "x * (x * y) = (z * y) * w", "equation2": "x * (y * x) = (z * z) * x", "answer": false}
|
| 196 |
+
{"id": "hard2_0196", "index": 196, "difficulty": "hard", "eq1_id": 2531, "eq2_id": 849, "equation1": "x = (y * ((y * x) * x)) * y", "equation2": "x = x * ((y * y) * (z * y))", "answer": false}
|
| 197 |
+
{"id": "hard2_0197", "index": 197, "difficulty": "hard", "eq1_id": 3295, "eq2_id": 3290, "equation1": "x * x = y * (z * (y * w))", "equation2": "x * x = y * (z * (x * z))", "answer": false}
|
| 198 |
+
{"id": "hard2_0198", "index": 198, "difficulty": "hard", "eq1_id": 3396, "eq2_id": 3846, "equation1": "x * y = z * (y * (x * x))", "equation2": "x * y = (z * w) * (z * x)", "answer": true}
|
| 199 |
+
{"id": "hard2_0199", "index": 199, "difficulty": "hard", "eq1_id": 2668, "eq2_id": 2848, "equation1": "x = ((x * y) * (x * z)) * w", "equation2": "x = ((x * (x * x)) * x) * y", "answer": true}
|
| 200 |
+
{"id": "hard2_0200", "index": 200, "difficulty": "hard", "eq1_id": 3365, "eq2_id": 3987, "equation1": "x * y = y * (z * (x * w))", "equation2": "x * y = (y * (z * w)) * u", "answer": true}
|
data/hard3.jsonl
ADDED
|
@@ -0,0 +1,400 @@
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| 1 |
+
{"id": "hard3_0001", "index": 1, "difficulty": "hard", "eq1_id": 5, "eq2_id": 625, "equation1": "x = y * x", "equation2": "x = x * (x * ((y * z) * x))", "answer": true}
|
| 2 |
+
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|
| 3 |
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{"id": "hard3_0003", "index": 3, "difficulty": "hard", "eq1_id": 13, "eq2_id": 583, "equation1": "x = y * (x * x)", "equation2": "x = y * (z * (z * (w * x)))", "answer": true}
|
| 4 |
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{"id": "hard3_0004", "index": 4, "difficulty": "hard", "eq1_id": 22, "eq2_id": 4347, "equation1": "x = y * (z * w)", "equation2": "x * (y * y) = y * (z * w)", "answer": true}
|
| 5 |
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{"id": "hard3_0005", "index": 5, "difficulty": "hard", "eq1_id": 34, "eq2_id": 3556, "equation1": "x = (y * z) * x", "equation2": "x * y = y * ((y * x) * y)", "answer": true}
|
| 6 |
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{"id": "hard3_0006", "index": 6, "difficulty": "hard", "eq1_id": 38, "eq2_id": 4271, "equation1": "x * x = x * y", "equation2": "x * (x * x) = x * (y * z)", "answer": true}
|
| 7 |
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{"id": "hard3_0007", "index": 7, "difficulty": "hard", "eq1_id": 38, "eq2_id": 4517, "equation1": "x * x = x * y", "equation2": "x * (y * z) = (x * z) * w", "answer": false}
|
| 8 |
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{"id": "hard3_0008", "index": 8, "difficulty": "hard", "eq1_id": 41, "eq2_id": 4407, "equation1": "x * x = y * z", "equation2": "x * (x * y) = (y * x) * z", "answer": true}
|
| 9 |
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{"id": "hard3_0009", "index": 9, "difficulty": "hard", "eq1_id": 48, "eq2_id": 2255, "equation1": "x = x * (x * (x * y))", "equation2": "x = (x * (y * (x * x))) * z", "answer": false}
|
| 10 |
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{"id": "hard3_0010", "index": 10, "difficulty": "hard", "eq1_id": 49, "eq2_id": 3867, "equation1": "x = x * (x * (y * x))", "equation2": "x * x = (x * (y * x)) * x", "answer": false}
|
| 11 |
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{"id": "hard3_0011", "index": 11, "difficulty": "hard", "eq1_id": 51, "eq2_id": 2862, "equation1": "x = x * (x * (y * z))", "equation2": "x = ((x * (y * x)) * x) * x", "answer": false}
|
| 12 |
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{"id": "hard3_0012", "index": 12, "difficulty": "hard", "eq1_id": 52, "eq2_id": 3664, "equation1": "x = x * (y * (x * x))", "equation2": "x * x = (x * y) * (x * x)", "answer": false}
|
| 13 |
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{"id": "hard3_0013", "index": 13, "difficulty": "hard", "eq1_id": 58, "eq2_id": 3050, "equation1": "x = x * (y * (z * x))", "equation2": "x = (((x * x) * x) * x) * x", "answer": false}
|
| 14 |
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{"id": "hard3_0014", "index": 14, "difficulty": "hard", "eq1_id": 59, "eq2_id": 3086, "equation1": "x = x * (y * (z * y))", "equation2": "x = (((x * y) * z) * x) * y", "answer": true}
|
| 15 |
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{"id": "hard3_0015", "index": 15, "difficulty": "hard", "eq1_id": 60, "eq2_id": 3332, "equation1": "x = x * (y * (z * z))", "equation2": "x * y = x * (z * (y * w))", "answer": true}
|
| 16 |
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{"id": "hard3_0016", "index": 16, "difficulty": "hard", "eq1_id": 62, "eq2_id": 3762, "equation1": "x = y * (x * (x * x))", "equation2": "x * y = (y * y) * (y * y)", "answer": false}
|
| 17 |
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{"id": "hard3_0017", "index": 17, "difficulty": "hard", "eq1_id": 72, "eq2_id": 214, "equation1": "x = y * (y * (x * x))", "equation2": "x = (x * (y * z)) * x", "answer": false}
|
| 18 |
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{"id": "hard3_0018", "index": 18, "difficulty": "hard", "eq1_id": 72, "eq2_id": 554, "equation1": "x = y * (y * (x * x))", "equation2": "x = y * (z * (y * (x * x)))", "answer": false}
|
| 19 |
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{"id": "hard3_0019", "index": 19, "difficulty": "hard", "eq1_id": 78, "eq2_id": 1405, "equation1": "x = y * (y * (z * x))", "equation2": "x = y * (((z * w) * y) * x)", "answer": false}
|
| 20 |
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{"id": "hard3_0020", "index": 20, "difficulty": "hard", "eq1_id": 90, "eq2_id": 1428, "equation1": "x = y * (z * (z * x))", "equation2": "x = (x * x) * (x * (y * x))", "answer": true}
|
| 21 |
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{"id": "hard3_0021", "index": 21, "difficulty": "hard", "eq1_id": 100, "eq2_id": 845, "equation1": "x = x * ((x * x) * y)", "equation2": "x = x * ((y * y) * (y * x))", "answer": false}
|
| 22 |
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{"id": "hard3_0022", "index": 22, "difficulty": "hard", "eq1_id": 103, "eq2_id": 3519, "equation1": "x = x * ((x * y) * z)", "equation2": "x * y = x * ((y * x) * y)", "answer": false}
|
| 23 |
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{"id": "hard3_0023", "index": 23, "difficulty": "hard", "eq1_id": 110, "eq2_id": 10, "equation1": "x = x * ((y * z) * x)", "equation2": "x = x * (y * x)", "answer": true}
|
| 24 |
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{"id": "hard3_0024", "index": 24, "difficulty": "hard", "eq1_id": 112, "eq2_id": 2277, "equation1": "x = x * ((y * z) * z)", "equation2": "x = (x * (y * (z * y))) * x", "answer": true}
|
| 25 |
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{"id": "hard3_0025", "index": 25, "difficulty": "hard", "eq1_id": 124, "eq2_id": 1776, "equation1": "x = y * ((y * x) * x)", "equation2": "x = (y * z) * ((y * y) * x)", "answer": false}
|
| 26 |
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{"id": "hard3_0026", "index": 26, "difficulty": "hard", "eq1_id": 127, "eq2_id": 2148, "equation1": "x = y * ((y * y) * x)", "equation2": "x = ((y * y) * z) * (y * x)", "answer": false}
|
| 27 |
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{"id": "hard3_0027", "index": 27, "difficulty": "hard", "eq1_id": 134, "eq2_id": 176, "equation1": "x = y * ((z * x) * x)", "equation2": "x = (y * y) * (x * x)", "answer": true}
|
| 28 |
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{"id": "hard3_0028", "index": 28, "difficulty": "hard", "eq1_id": 134, "eq2_id": 2222, "equation1": "x = y * ((z * x) * x)", "equation2": "x = ((y * z) * w) * (z * x)", "answer": true}
|
| 29 |
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{"id": "hard3_0029", "index": 29, "difficulty": "hard", "eq1_id": 138, "eq2_id": 4183, "equation1": "x = y * ((z * y) * x)", "equation2": "x * y = ((y * z) * z) * y", "answer": false}
|
| 30 |
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{"id": "hard3_0030", "index": 30, "difficulty": "hard", "eq1_id": 155, "eq2_id": 3509, "equation1": "x = (x * x) * (y * z)", "equation2": "x * y = x * ((x * x) * y)", "answer": true}
|
| 31 |
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{"id": "hard3_0031", "index": 31, "difficulty": "hard", "eq1_id": 156, "eq2_id": 3334, "equation1": "x = (x * y) * (x * x)", "equation2": "x * y = x * (z * (z * y))", "answer": false}
|
| 32 |
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{"id": "hard3_0032", "index": 32, "difficulty": "hard", "eq1_id": 168, "eq2_id": 3935, "equation1": "x = (y * x) * (x * z)", "equation2": "x * y = (x * (z * x)) * y", "answer": false}
|
| 33 |
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{"id": "hard3_0033", "index": 33, "difficulty": "hard", "eq1_id": 172, "eq2_id": 4080, "equation1": "x = (y * x) * (z * x)", "equation2": "x * x = ((y * x) * x) * x", "answer": true}
|
| 34 |
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{"id": "hard3_0034", "index": 34, "difficulty": "hard", "eq1_id": 176, "eq2_id": 1096, "equation1": "x = (y * y) * (x * x)", "equation2": "x = y * ((x * (z * y)) * x)", "answer": true}
|
| 35 |
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{"id": "hard3_0035", "index": 35, "difficulty": "hard", "eq1_id": 194, "eq2_id": 1075, "equation1": "x = (y * z) * (z * x)", "equation2": "x = y * ((x * (x * y)) * x)", "answer": false}
|
| 36 |
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{"id": "hard3_0036", "index": 36, "difficulty": "hard", "eq1_id": 204, "eq2_id": 1426, "equation1": "x = (x * (x * x)) * y", "equation2": "x = (x * x) * (x * (x * x))", "answer": true}
|
| 37 |
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{"id": "hard3_0037", "index": 37, "difficulty": "hard", "eq1_id": 205, "eq2_id": 3464, "equation1": "x = (x * (x * y)) * x", "equation2": "x * x = x * ((y * y) * x)", "answer": false}
|
| 38 |
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{"id": "hard3_0038", "index": 38, "difficulty": "hard", "eq1_id": 207, "eq2_id": 3256, "equation1": "x = (x * (x * y)) * z", "equation2": "x * x = x * (x * (y * y))", "answer": true}
|
| 39 |
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{"id": "hard3_0039", "index": 39, "difficulty": "hard", "eq1_id": 209, "eq2_id": 1430, "equation1": "x = (x * (y * x)) * y", "equation2": "x = (x * x) * (x * (y * z))", "answer": false}
|
| 40 |
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{"id": "hard3_0040", "index": 40, "difficulty": "hard", "eq1_id": 215, "eq2_id": 3050, "equation1": "x = (x * (y * z)) * y", "equation2": "x = (((x * x) * x) * x) * x", "answer": false}
|
| 41 |
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{"id": "hard3_0041", "index": 41, "difficulty": "hard", "eq1_id": 256, "eq2_id": 2477, "equation1": "x = ((x * x) * x) * y", "equation2": "x = (x * ((y * z) * x)) * y", "answer": false}
|
| 42 |
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{"id": "hard3_0042", "index": 42, "difficulty": "hard", "eq1_id": 258, "eq2_id": 851, "equation1": "x = ((x * x) * y) * y", "equation2": "x = x * ((y * y) * (z * w))", "answer": false}
|
| 43 |
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{"id": "hard3_0043", "index": 43, "difficulty": "hard", "eq1_id": 259, "eq2_id": 2684, "equation1": "x = ((x * x) * y) * z", "equation2": "x = ((x * y) * (z * y)) * y", "answer": true}
|
| 44 |
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{"id": "hard3_0044", "index": 44, "difficulty": "hard", "eq1_id": 269, "eq2_id": 3949, "equation1": "x = ((x * y) * z) * w", "equation2": "x * y = (x * (z * w)) * w", "answer": false}
|
| 45 |
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{"id": "hard3_0045", "index": 45, "difficulty": "hard", "eq1_id": 273, "eq2_id": 4362, "equation1": "x = ((y * x) * y) * x", "equation2": "x * (y * z) = y * (x * z)", "answer": false}
|
| 46 |
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{"id": "hard3_0046", "index": 46, "difficulty": "hard", "eq1_id": 294, "eq2_id": 2318, "equation1": "x = ((y * z) * y) * x", "equation2": "x = (y * (x * (z * z))) * x", "answer": true}
|
| 47 |
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{"id": "hard3_0047", "index": 47, "difficulty": "hard", "eq1_id": 294, "eq2_id": 4155, "equation1": "x = ((y * z) * y) * x", "equation2": "x * y = ((y * x) * x) * y", "answer": true}
|
| 48 |
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{"id": "hard3_0048", "index": 48, "difficulty": "hard", "eq1_id": 298, "eq2_id": 4564, "equation1": "x = ((y * z) * z) * x", "equation2": "x * (y * z) = (w * y) * z", "answer": true}
|
| 49 |
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{"id": "hard3_0049", "index": 49, "difficulty": "hard", "eq1_id": 302, "eq2_id": 549, "equation1": "x = ((y * z) * w) * x", "equation2": "x = y * (z * (x * (w * x)))", "answer": true}
|
| 50 |
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{"id": "hard3_0050", "index": 50, "difficulty": "hard", "eq1_id": 315, "eq2_id": 4196, "equation1": "x * x = y * (y * x)", "equation2": "x * y = ((z * x) * y) * y", "answer": false}
|
| 51 |
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{"id": "hard3_0051", "index": 51, "difficulty": "hard", "eq1_id": 344, "eq2_id": 3965, "equation1": "x * y = z * (x * z)", "equation2": "x * y = (y * (y * y)) * y", "answer": true}
|
| 52 |
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{"id": "hard3_0052", "index": 52, "difficulty": "hard", "eq1_id": 348, "eq2_id": 3734, "equation1": "x * y = z * (y * z)", "equation2": "x * y = (x * z) * (x * w)", "answer": true}
|
| 53 |
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{"id": "hard3_0053", "index": 53, "difficulty": "hard", "eq1_id": 348, "eq2_id": 4367, "equation1": "x * y = z * (y * z)", "equation2": "x * (y * z) = y * (w * z)", "answer": true}
|
| 54 |
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{"id": "hard3_0054", "index": 54, "difficulty": "hard", "eq1_id": 353, "eq2_id": 3950, "equation1": "x * y = z * (z * w)", "equation2": "x * y = (x * (z * w)) * u", "answer": true}
|
| 55 |
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{"id": "hard3_0055", "index": 55, "difficulty": "hard", "eq1_id": 363, "eq2_id": 4118, "equation1": "x * x = (x * y) * z", "equation2": "x * y = ((x * x) * x) * y", "answer": false}
|
| 56 |
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{"id": "hard3_0056", "index": 56, "difficulty": "hard", "eq1_id": 366, "eq2_id": 4288, "equation1": "x * x = (y * x) * z", "equation2": "x * (x * y) = x * (z * z)", "answer": false}
|
| 57 |
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{"id": "hard3_0057", "index": 57, "difficulty": "hard", "eq1_id": 372, "eq2_id": 315, "equation1": "x * x = (y * z) * z", "equation2": "x * x = y * (y * x)", "answer": false}
|
| 58 |
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{"id": "hard3_0058", "index": 58, "difficulty": "hard", "eq1_id": 373, "eq2_id": 359, "equation1": "x * x = (y * z) * w", "equation2": "x * x = (x * x) * x", "answer": true}
|
| 59 |
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{"id": "hard3_0059", "index": 59, "difficulty": "hard", "eq1_id": 373, "eq2_id": 4416, "equation1": "x * x = (y * z) * w", "equation2": "x * (x * y) = (z * x) * y", "answer": false}
|
| 60 |
+
{"id": "hard3_0060", "index": 60, "difficulty": "hard", "eq1_id": 402, "eq2_id": 3855, "equation1": "x * y = (z * z) * x", "equation2": "x * y = (z * w) * (w * u)", "answer": true}
|
| 61 |
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{"id": "hard3_0061", "index": 61, "difficulty": "hard", "eq1_id": 404, "eq2_id": 3339, "equation1": "x * y = (z * z) * z", "equation2": "x * y = x * (z * (w * z))", "answer": true}
|
| 62 |
+
{"id": "hard3_0062", "index": 62, "difficulty": "hard", "eq1_id": 419, "eq2_id": 842, "equation1": "x = x * (x * (y * (y * x)))", "equation2": "x = x * ((y * y) * (x * x))", "answer": false}
|
| 63 |
+
{"id": "hard3_0063", "index": 63, "difficulty": "hard", "eq1_id": 423, "eq2_id": 1070, "equation1": "x = x * (x * (y * (z * y)))", "equation2": "x = x * ((y * (z * w)) * w)", "answer": false}
|
| 64 |
+
{"id": "hard3_0064", "index": 64, "difficulty": "hard", "eq1_id": 424, "eq2_id": 2466, "equation1": "x = x * (x * (y * (z * z)))", "equation2": "x = (x * ((y * y) * x)) * x", "answer": false}
|
| 65 |
+
{"id": "hard3_0065", "index": 65, "difficulty": "hard", "eq1_id": 428, "eq2_id": 360, "equation1": "x = x * (y * (x * (x * z)))", "equation2": "x * x = (x * x) * y", "answer": false}
|
| 66 |
+
{"id": "hard3_0066", "index": 66, "difficulty": "hard", "eq1_id": 435, "eq2_id": 1678, "equation1": "x = x * (y * (x * (z * w)))", "equation2": "x = (x * y) * ((z * w) * z)", "answer": true}
|
| 67 |
+
{"id": "hard3_0067", "index": 67, "difficulty": "hard", "eq1_id": 453, "eq2_id": 615, "equation1": "x = x * (y * (z * (y * w)))", "equation2": "x = x * (x * ((x * x) * y))", "answer": true}
|
| 68 |
+
{"id": "hard3_0068", "index": 68, "difficulty": "hard", "eq1_id": 456, "eq2_id": 1051, "equation1": "x = x * (y * (z * (z * z)))", "equation2": "x = x * ((y * (y * z)) * x)", "answer": true}
|
| 69 |
+
{"id": "hard3_0069", "index": 69, "difficulty": "hard", "eq1_id": 483, "eq2_id": 2087, "equation1": "x = y * (x * (z * (x * x)))", "equation2": "x = ((y * x) * x) * (x * x)", "answer": false}
|
| 70 |
+
{"id": "hard3_0070", "index": 70, "difficulty": "hard", "eq1_id": 487, "eq2_id": 114, "equation1": "x = y * (x * (z * (y * x)))", "equation2": "x = y * ((x * x) * x)", "answer": false}
|
| 71 |
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{"id": "hard3_0071", "index": 71, "difficulty": "hard", "eq1_id": 511, "eq2_id": 2132, "equation1": "x = y * (y * (y * (x * y)))", "equation2": "x = ((y * y) * x) * (z * z)", "answer": false}
|
| 72 |
+
{"id": "hard3_0072", "index": 72, "difficulty": "hard", "eq1_id": 511, "eq2_id": 3211, "equation1": "x = y * (y * (y * (x * y)))", "equation2": "x = (((y * z) * z) * x) * y", "answer": false}
|
| 73 |
+
{"id": "hard3_0073", "index": 73, "difficulty": "hard", "eq1_id": 541, "eq2_id": 1366, "equation1": "x = y * (z * (x * (y * x)))", "equation2": "x = y * (((z * y) * x) * x)", "answer": false}
|
| 74 |
+
{"id": "hard3_0074", "index": 74, "difficulty": "hard", "eq1_id": 545, "eq2_id": 1832, "equation1": "x = y * (z * (x * (z * x)))", "equation2": "x = (x * (x * x)) * (x * x)", "answer": false}
|
| 75 |
+
{"id": "hard3_0075", "index": 75, "difficulty": "hard", "eq1_id": 545, "eq2_id": 2043, "equation1": "x = y * (z * (x * (z * x)))", "equation2": "x = ((x * x) * y) * (y * x)", "answer": false}
|
| 76 |
+
{"id": "hard3_0076", "index": 76, "difficulty": "hard", "eq1_id": 549, "eq2_id": 1966, "equation1": "x = y * (z * (x * (w * x)))", "equation2": "x = (y * (z * x)) * (z * x)", "answer": false}
|
| 77 |
+
{"id": "hard3_0077", "index": 77, "difficulty": "hard", "eq1_id": 554, "eq2_id": 3935, "equation1": "x = y * (z * (y * (x * x)))", "equation2": "x * y = (x * (z * x)) * y", "answer": true}
|
| 78 |
+
{"id": "hard3_0078", "index": 78, "difficulty": "hard", "eq1_id": 556, "eq2_id": 4396, "equation1": "x = y * (z * (y * (x * z)))", "equation2": "x * (x * y) = (x * x) * y", "answer": false}
|
| 79 |
+
{"id": "hard3_0079", "index": 79, "difficulty": "hard", "eq1_id": 579, "eq2_id": 2144, "equation1": "x = y * (z * (z * (z * x)))", "equation2": "x = ((y * y) * z) * (x * x)", "answer": false}
|
| 80 |
+
{"id": "hard3_0080", "index": 80, "difficulty": "hard", "eq1_id": 618, "eq2_id": 3310, "equation1": "x = x * (x * ((x * y) * z))", "equation2": "x * y = x * (x * (y * z))", "answer": false}
|
| 81 |
+
{"id": "hard3_0081", "index": 81, "difficulty": "hard", "eq1_id": 623, "eq2_id": 1035, "equation1": "x = x * (x * ((y * y) * y))", "equation2": "x = x * ((y * (x * x)) * x)", "answer": false}
|
| 82 |
+
{"id": "hard3_0082", "index": 82, "difficulty": "hard", "eq1_id": 625, "eq2_id": 2646, "equation1": "x = x * (x * ((y * z) * x))", "equation2": "x = ((x * x) * (x * y)) * x", "answer": false}
|
| 83 |
+
{"id": "hard3_0083", "index": 83, "difficulty": "hard", "eq1_id": 626, "eq2_id": 3744, "equation1": "x = x * (x * ((y * z) * y))", "equation2": "x * y = (x * z) * (w * y)", "answer": false}
|
| 84 |
+
{"id": "hard3_0084", "index": 84, "difficulty": "hard", "eq1_id": 627, "eq2_id": 3869, "equation1": "x = x * (x * ((y * z) * z))", "equation2": "x * x = (x * (y * x)) * z", "answer": false}
|
| 85 |
+
{"id": "hard3_0085", "index": 85, "difficulty": "hard", "eq1_id": 644, "eq2_id": 2462, "equation1": "x = x * (y * ((y * y) * z))", "equation2": "x = (x * ((y * x) * z)) * x", "answer": true}
|
| 86 |
+
{"id": "hard3_0086", "index": 86, "difficulty": "hard", "eq1_id": 646, "eq2_id": 4144, "equation1": "x = x * (y * ((y * z) * y))", "equation2": "x * y = ((x * z) * y) * w", "answer": false}
|
| 87 |
+
{"id": "hard3_0087", "index": 87, "difficulty": "hard", "eq1_id": 648, "eq2_id": 3067, "equation1": "x = x * (y * ((y * z) * w))", "equation2": "x = (((x * y) * x) * x) * z", "answer": true}
|
| 88 |
+
{"id": "hard3_0088", "index": 88, "difficulty": "hard", "eq1_id": 648, "eq2_id": 3869, "equation1": "x = x * (y * ((y * z) * w))", "equation2": "x * x = (x * (y * x)) * z", "answer": true}
|
| 89 |
+
{"id": "hard3_0089", "index": 89, "difficulty": "hard", "eq1_id": 652, "eq2_id": 3266, "equation1": "x = x * (y * ((z * x) * w))", "equation2": "x * x = x * (y * (z * z))", "answer": true}
|
| 90 |
+
{"id": "hard3_0090", "index": 90, "difficulty": "hard", "eq1_id": 660, "eq2_id": 1848, "equation1": "x = x * (y * ((z * z) * w))", "equation2": "x = (x * (y * x)) * (x * y)", "answer": true}
|
| 91 |
+
{"id": "hard3_0091", "index": 91, "difficulty": "hard", "eq1_id": 707, "eq2_id": 1996, "equation1": "x = y * (y * ((x * y) * y))", "equation2": "x = (y * (z * z)) * (y * x)", "answer": false}
|
| 92 |
+
{"id": "hard3_0092", "index": 92, "difficulty": "hard", "eq1_id": 707, "eq2_id": 4090, "equation1": "x = y * (y * ((x * y) * y))", "equation2": "x * x = ((y * y) * x) * x", "answer": false}
|
| 93 |
+
{"id": "hard3_0093", "index": 93, "difficulty": "hard", "eq1_id": 714, "eq2_id": 1075, "equation1": "x = y * (y * ((y * x) * y))", "equation2": "x = y * ((x * (x * y)) * x)", "answer": false}
|
| 94 |
+
{"id": "hard3_0094", "index": 94, "difficulty": "hard", "eq1_id": 723, "eq2_id": 3089, "equation1": "x = y * (y * ((z * x) * x))", "equation2": "x = (((x * y) * z) * y) * x", "answer": false}
|
| 95 |
+
{"id": "hard3_0095", "index": 95, "difficulty": "hard", "eq1_id": 735, "eq2_id": 2812, "equation1": "x = y * (y * ((z * w) * x))", "equation2": "x = ((y * z) * (z * z)) * x", "answer": false}
|
| 96 |
+
{"id": "hard3_0096", "index": 96, "difficulty": "hard", "eq1_id": 752, "eq2_id": 203, "equation1": "x = y * (z * ((x * w) * x))", "equation2": "x = (x * (x * x)) * x", "answer": false}
|
| 97 |
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{"id": "hard3_0097", "index": 97, "difficulty": "hard", "eq1_id": 752, "eq2_id": 2554, "equation1": "x = y * (z * ((x * w) * x))", "equation2": "x = (y * ((y * z) * y)) * x", "answer": false}
|
| 98 |
+
{"id": "hard3_0098", "index": 98, "difficulty": "hard", "eq1_id": 761, "eq2_id": 2037, "equation1": "x = y * (z * ((y * y) * x))", "equation2": "x = ((x * x) * x) * (y * x)", "answer": false}
|
| 99 |
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{"id": "hard3_0099", "index": 99, "difficulty": "hard", "eq1_id": 761, "eq2_id": 2862, "equation1": "x = y * (z * ((y * y) * x))", "equation2": "x = ((x * (y * x)) * x) * x", "answer": false}
|
| 100 |
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{"id": "hard3_0100", "index": 100, "difficulty": "hard", "eq1_id": 796, "eq2_id": 1115, "equation1": "x = y * (z * ((w * y) * x))", "equation2": "x = y * ((y * (x * z)) * x)", "answer": false}
|
| 101 |
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{"id": "hard3_0101", "index": 101, "difficulty": "hard", "eq1_id": 796, "eq2_id": 2165, "equation1": "x = y * (z * ((w * y) * x))", "equation2": "x = ((y * z) * x) * (y * x)", "answer": false}
|
| 102 |
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{"id": "hard3_0102", "index": 102, "difficulty": "hard", "eq1_id": 806, "eq2_id": 2868, "equation1": "x = y * (z * ((w * w) * x))", "equation2": "x = ((x * (y * x)) * z) * x", "answer": false}
|
| 103 |
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{"id": "hard3_0103", "index": 103, "difficulty": "hard", "eq1_id": 827, "eq2_id": 3332, "equation1": "x = x * ((x * y) * (y * z))", "equation2": "x * y = x * (z * (y * w))", "answer": false}
|
| 104 |
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{"id": "hard3_0104", "index": 104, "difficulty": "hard", "eq1_id": 829, "eq2_id": 4477, "equation1": "x = x * ((x * y) * (z * y))", "equation2": "x * (y * y) = (x * z) * z", "answer": false}
|
| 105 |
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{"id": "hard3_0105", "index": 105, "difficulty": "hard", "eq1_id": 830, "eq2_id": 3327, "equation1": "x = x * ((x * y) * (z * z))", "equation2": "x * y = x * (z * (x * z))", "answer": false}
|
| 106 |
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{"id": "hard3_0106", "index": 106, "difficulty": "hard", "eq1_id": 853, "eq2_id": 160, "equation1": "x = x * ((y * z) * (x * y))", "equation2": "x = (x * y) * (y * y)", "answer": true}
|
| 107 |
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{"id": "hard3_0107", "index": 107, "difficulty": "hard", "eq1_id": 859, "eq2_id": 2878, "equation1": "x = x * ((y * z) * (y * w))", "equation2": "x = ((x * (y * y)) * z) * x", "answer": true}
|
| 108 |
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{"id": "hard3_0108", "index": 108, "difficulty": "hard", "eq1_id": 860, "eq2_id": 4316, "equation1": "x = x * ((y * z) * (z * x))", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 109 |
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{"id": "hard3_0109", "index": 109, "difficulty": "hard", "eq1_id": 867, "eq2_id": 4632, "equation1": "x = x * ((y * z) * (w * w))", "equation2": "(x * y) * x = (x * z) * y", "answer": true}
|
| 110 |
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{"id": "hard3_0110", "index": 110, "difficulty": "hard", "eq1_id": 885, "eq2_id": 2939, "equation1": "x = y * ((x * y) * (z * x))", "equation2": "x = ((y * (y * x)) * y) * x", "answer": false}
|
| 111 |
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{"id": "hard3_0111", "index": 111, "difficulty": "hard", "eq1_id": 897, "eq2_id": 3467, "equation1": "x = y * ((x * z) * (z * x))", "equation2": "x * x = x * ((y * z) * x)", "answer": false}
|
| 112 |
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{"id": "hard3_0112", "index": 112, "difficulty": "hard", "eq1_id": 906, "eq2_id": 1231, "equation1": "x = y * ((y * x) * (x * x))", "equation2": "x = x * (((x * y) * y) * x)", "answer": false}
|
| 113 |
+
{"id": "hard3_0113", "index": 113, "difficulty": "hard", "eq1_id": 916, "eq2_id": 1238, "equation1": "x = y * ((y * y) * (x * x))", "equation2": "x = x * (((y * x) * x) * x)", "answer": false}
|
| 114 |
+
{"id": "hard3_0114", "index": 114, "difficulty": "hard", "eq1_id": 922, "eq2_id": 1444, "equation1": "x = y * ((y * y) * (z * x))", "equation2": "x = (x * y) * (x * (y * x))", "answer": true}
|
| 115 |
+
{"id": "hard3_0115", "index": 115, "difficulty": "hard", "eq1_id": 926, "eq2_id": 1502, "equation1": "x = y * ((y * z) * (x * x))", "equation2": "x = (y * x) * (z * (y * x))", "answer": true}
|
| 116 |
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{"id": "hard3_0116", "index": 116, "difficulty": "hard", "eq1_id": 930, "eq2_id": 2998, "equation1": "x = y * ((y * z) * (y * x))", "equation2": "x = ((y * (z * y)) * z) * x", "answer": false}
|
| 117 |
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{"id": "hard3_0117", "index": 117, "difficulty": "hard", "eq1_id": 943, "eq2_id": 3962, "equation1": "x = y * ((z * x) * (x * x))", "equation2": "x * y = (y * (y * x)) * y", "answer": true}
|
| 118 |
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{"id": "hard3_0118", "index": 118, "difficulty": "hard", "eq1_id": 947, "eq2_id": 3126, "equation1": "x = y * ((z * x) * (y * x))", "equation2": "x = (((y * x) * z) * y) * x", "answer": false}
|
| 119 |
+
{"id": "hard3_0119", "index": 119, "difficulty": "hard", "eq1_id": 977, "eq2_id": 1231, "equation1": "x = y * ((z * z) * (x * x))", "equation2": "x = x * (((x * y) * y) * x)", "answer": false}
|
| 120 |
+
{"id": "hard3_0120", "index": 120, "difficulty": "hard", "eq1_id": 977, "eq2_id": 1860, "equation1": "x = y * ((z * z) * (x * x))", "equation2": "x = (x * (y * y)) * (y * x)", "answer": false}
|
| 121 |
+
{"id": "hard3_0121", "index": 121, "difficulty": "hard", "eq1_id": 994, "eq2_id": 2628, "equation1": "x = y * ((z * w) * (x * x))", "equation2": "x = (y * ((z * w) * z)) * x", "answer": false}
|
| 122 |
+
{"id": "hard3_0122", "index": 122, "difficulty": "hard", "eq1_id": 1009, "eq2_id": 130, "equation1": "x = y * ((z * w) * (w * x))", "equation2": "x = y * ((y * z) * x)", "answer": false}
|
| 123 |
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{"id": "hard3_0123", "index": 123, "difficulty": "hard", "eq1_id": 1014, "eq2_id": 355, "equation1": "x = y * ((z * w) * (u * x))", "equation2": "x * y = z * (w * y)", "answer": false}
|
| 124 |
+
{"id": "hard3_0124", "index": 124, "difficulty": "hard", "eq1_id": 1014, "eq2_id": 1577, "equation1": "x = y * ((z * w) * (u * x))", "equation2": "x = (y * z) * (y * (z * x))", "answer": true}
|
| 125 |
+
{"id": "hard3_0125", "index": 125, "difficulty": "hard", "eq1_id": 1014, "eq2_id": 2318, "equation1": "x = y * ((z * w) * (u * x))", "equation2": "x = (y * (x * (z * z))) * x", "answer": false}
|
| 126 |
+
{"id": "hard3_0126", "index": 126, "difficulty": "hard", "eq1_id": 1014, "eq2_id": 2480, "equation1": "x = y * ((z * w) * (u * x))", "equation2": "x = (x * ((y * z) * y)) * x", "answer": false}
|
| 127 |
+
{"id": "hard3_0127", "index": 127, "difficulty": "hard", "eq1_id": 1014, "eq2_id": 4158, "equation1": "x = y * ((z * w) * (u * x))", "equation2": "x * y = ((y * x) * y) * y", "answer": true}
|
| 128 |
+
{"id": "hard3_0128", "index": 128, "difficulty": "hard", "eq1_id": 1032, "eq2_id": 2076, "equation1": "x = x * ((x * (y * z)) * y)", "equation2": "x = ((x * y) * z) * (y * z)", "answer": false}
|
| 129 |
+
{"id": "hard3_0129", "index": 129, "difficulty": "hard", "eq1_id": 1034, "eq2_id": 4630, "equation1": "x = x * ((x * (y * z)) * w)", "equation2": "(x * y) * x = (x * y) * z", "answer": false}
|
| 130 |
+
{"id": "hard3_0130", "index": 130, "difficulty": "hard", "eq1_id": 1037, "eq2_id": 3533, "equation1": "x = x * ((y * (x * x)) * z)", "equation2": "x * y = x * ((z * y) * y)", "answer": false}
|
| 131 |
+
{"id": "hard3_0131", "index": 131, "difficulty": "hard", "eq1_id": 1047, "eq2_id": 1463, "equation1": "x = x * ((y * (y * x)) * z)", "equation2": "x = (x * y) * (z * (x * z))", "answer": true}
|
| 132 |
+
{"id": "hard3_0132", "index": 132, "difficulty": "hard", "eq1_id": 1050, "eq2_id": 3320, "equation1": "x = x * ((y * (y * y)) * z)", "equation2": "x * y = x * (y * (y * z))", "answer": false}
|
| 133 |
+
{"id": "hard3_0133", "index": 133, "difficulty": "hard", "eq1_id": 1054, "eq2_id": 2264, "equation1": "x = x * ((y * (y * z)) * w)", "equation2": "x = (x * (y * (y * x))) * y", "answer": true}
|
| 134 |
+
{"id": "hard3_0134", "index": 134, "difficulty": "hard", "eq1_id": 1057, "eq2_id": 329, "equation1": "x = x * ((y * (z * x)) * z)", "equation2": "x * y = x * (z * y)", "answer": true}
|
| 135 |
+
{"id": "hard3_0135", "index": 135, "difficulty": "hard", "eq1_id": 1057, "eq2_id": 1454, "equation1": "x = x * ((y * (z * x)) * z)", "equation2": "x = (x * y) * (y * (y * x))", "answer": true}
|
| 136 |
+
{"id": "hard3_0136", "index": 136, "difficulty": "hard", "eq1_id": 1062, "eq2_id": 4271, "equation1": "x = x * ((y * (z * y)) * w)", "equation2": "x * (x * x) = x * (y * z)", "answer": true}
|
| 137 |
+
{"id": "hard3_0137", "index": 137, "difficulty": "hard", "eq1_id": 1065, "eq2_id": 1647, "equation1": "x = x * ((y * (z * z)) * z)", "equation2": "x = (x * y) * ((x * y) * x)", "answer": true}
|
| 138 |
+
{"id": "hard3_0138", "index": 138, "difficulty": "hard", "eq1_id": 1071, "eq2_id": 4631, "equation1": "x = x * ((y * (z * w)) * u)", "equation2": "(x * y) * x = (x * z) * x", "answer": true}
|
| 139 |
+
{"id": "hard3_0139", "index": 139, "difficulty": "hard", "eq1_id": 1072, "eq2_id": 107, "equation1": "x = y * ((x * (x * x)) * x)", "equation2": "x = x * ((y * y) * x)", "answer": true}
|
| 140 |
+
{"id": "hard3_0140", "index": 140, "difficulty": "hard", "eq1_id": 1072, "eq2_id": 1251, "equation1": "x = y * ((x * (x * x)) * x)", "equation2": "x = x * (((y * y) * y) * x)", "answer": true}
|
| 141 |
+
{"id": "hard3_0141", "index": 141, "difficulty": "hard", "eq1_id": 1085, "eq2_id": 4093, "equation1": "x = y * ((x * (y * y)) * x)", "equation2": "x * x = ((y * y) * y) * x", "answer": false}
|
| 142 |
+
{"id": "hard3_0142", "index": 142, "difficulty": "hard", "eq1_id": 1092, "eq2_id": 176, "equation1": "x = y * ((x * (z * x)) * x)", "equation2": "x = (y * y) * (x * x)", "answer": true}
|
| 143 |
+
{"id": "hard3_0143", "index": 143, "difficulty": "hard", "eq1_id": 1096, "eq2_id": 476, "equation1": "x = y * ((x * (z * y)) * x)", "equation2": "x = y * (x * (y * (y * x)))", "answer": false}
|
| 144 |
+
{"id": "hard3_0144", "index": 144, "difficulty": "hard", "eq1_id": 1125, "eq2_id": 2014, "equation1": "x = y * ((y * (y * z)) * x)", "equation2": "x = (y * (z * w)) * (y * x)", "answer": true}
|
| 145 |
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{"id": "hard3_0145", "index": 145, "difficulty": "hard", "eq1_id": 1181, "eq2_id": 1289, "equation1": "x = y * ((z * (z * x)) * y)", "equation2": "x = y * (((x * y) * y) * y)", "answer": true}
|
| 146 |
+
{"id": "hard3_0146", "index": 146, "difficulty": "hard", "eq1_id": 1181, "eq2_id": 1429, "equation1": "x = y * ((z * (z * x)) * y)", "equation2": "x = (x * x) * (x * (y * y))", "answer": false}
|
| 147 |
+
{"id": "hard3_0147", "index": 147, "difficulty": "hard", "eq1_id": 1212, "eq2_id": 1041, "equation1": "x = y * ((z * (w * w)) * x)", "equation2": "x = x * ((y * (x * z)) * x)", "answer": true}
|
| 148 |
+
{"id": "hard3_0148", "index": 148, "difficulty": "hard", "eq1_id": 1217, "eq2_id": 2056, "equation1": "x = y * ((z * (w * u)) * x)", "equation2": "x = ((x * y) * x) * (z * x)", "answer": true}
|
| 149 |
+
{"id": "hard3_0149", "index": 149, "difficulty": "hard", "eq1_id": 1232, "eq2_id": 3740, "equation1": "x = x * (((x * y) * y) * y)", "equation2": "x * y = (x * z) * (z * y)", "answer": false}
|
| 150 |
+
{"id": "hard3_0150", "index": 150, "difficulty": "hard", "eq1_id": 1243, "eq2_id": 1067, "equation1": "x = x * (((y * x) * y) * z)", "equation2": "x = x * ((y * (z * w)) * x)", "answer": false}
|
| 151 |
+
{"id": "hard3_0151", "index": 151, "difficulty": "hard", "eq1_id": 1243, "eq2_id": 4583, "equation1": "x = x * (((y * x) * y) * z)", "equation2": "(x * x) * x = (x * x) * y", "answer": false}
|
| 152 |
+
{"id": "hard3_0152", "index": 152, "difficulty": "hard", "eq1_id": 1252, "eq2_id": 1020, "equation1": "x = x * (((y * y) * y) * y)", "equation2": "x = x * ((x * (x * x)) * x)", "answer": false}
|
| 153 |
+
{"id": "hard3_0153", "index": 153, "difficulty": "hard", "eq1_id": 1259, "eq2_id": 4318, "equation1": "x = x * (((y * z) * x) * y)", "equation2": "x * (y * x) = x * (z * z)", "answer": false}
|
| 154 |
+
{"id": "hard3_0154", "index": 154, "difficulty": "hard", "eq1_id": 1281, "eq2_id": 3397, "equation1": "x = y * (((x * x) * z) * x)", "equation2": "x * y = z * (y * (x * y))", "answer": true}
|
| 155 |
+
{"id": "hard3_0155", "index": 155, "difficulty": "hard", "eq1_id": 1281, "eq2_id": 3409, "equation1": "x = y * (((x * x) * z) * x)", "equation2": "x * y = z * (y * (w * y))", "answer": true}
|
| 156 |
+
{"id": "hard3_0156", "index": 156, "difficulty": "hard", "eq1_id": 1318, "eq2_id": 2078, "equation1": "x = y * (((y * x) * z) * x)", "equation2": "x = ((x * y) * z) * (z * x)", "answer": true}
|
| 157 |
+
{"id": "hard3_0157", "index": 157, "difficulty": "hard", "eq1_id": 1328, "eq2_id": 1078, "equation1": "x = y * (((y * y) * z) * x)", "equation2": "x = y * ((x * (x * z)) * x)", "answer": true}
|
| 158 |
+
{"id": "hard3_0158", "index": 158, "difficulty": "hard", "eq1_id": 1332, "eq2_id": 1146, "equation1": "x = y * (((y * z) * x) * x)", "equation2": "x = y * ((z * (x * x)) * x)", "answer": true}
|
| 159 |
+
{"id": "hard3_0159", "index": 159, "difficulty": "hard", "eq1_id": 1340, "eq2_id": 4635, "equation1": "x = y * (((y * z) * z) * x)", "equation2": "(x * y) * x = (y * x) * x", "answer": false}
|
| 160 |
+
{"id": "hard3_0160", "index": 160, "difficulty": "hard", "eq1_id": 1433, "eq2_id": 4631, "equation1": "x = (x * x) * (y * (x * z))", "equation2": "(x * y) * x = (x * z) * x", "answer": true}
|
| 161 |
+
{"id": "hard3_0161", "index": 161, "difficulty": "hard", "eq1_id": 1458, "eq2_id": 1862, "equation1": "x = (x * y) * (y * (z * y))", "equation2": "x = (x * (y * y)) * (y * z)", "answer": false}
|
| 162 |
+
{"id": "hard3_0162", "index": 162, "difficulty": "hard", "eq1_id": 1462, "eq2_id": 4135, "equation1": "x = (x * y) * (z * (x * y))", "equation2": "x * y = ((x * y) * z) * z", "answer": true}
|
| 163 |
+
{"id": "hard3_0163", "index": 163, "difficulty": "hard", "eq1_id": 1480, "eq2_id": 528, "equation1": "x = (y * x) * (x * (x * z))", "equation2": "x = y * (y * (z * (z * x)))", "answer": false}
|
| 164 |
+
{"id": "hard3_0164", "index": 164, "difficulty": "hard", "eq1_id": 1484, "eq2_id": 2351, "equation1": "x = (y * x) * (x * (z * x))", "equation2": "x = (y * (y * (z * y))) * x", "answer": false}
|
| 165 |
+
{"id": "hard3_0165", "index": 165, "difficulty": "hard", "eq1_id": 1487, "eq2_id": 232, "equation1": "x = (y * x) * (x * (z * w))", "equation2": "x = (y * (y * y)) * y", "answer": false}
|
| 166 |
+
{"id": "hard3_0166", "index": 166, "difficulty": "hard", "eq1_id": 1487, "eq2_id": 287, "equation1": "x = (y * x) * (x * (z * w))", "equation2": "x = ((y * y) * z) * y", "answer": false}
|
| 167 |
+
{"id": "hard3_0167", "index": 167, "difficulty": "hard", "eq1_id": 1487, "eq2_id": 3389, "equation1": "x = (y * x) * (x * (z * w))", "equation2": "x * y = z * (x * (z * z))", "answer": false}
|
| 168 |
+
{"id": "hard3_0168", "index": 168, "difficulty": "hard", "eq1_id": 1506, "eq2_id": 359, "equation1": "x = (y * x) * (z * (z * x))", "equation2": "x * x = (x * x) * x", "answer": true}
|
| 169 |
+
{"id": "hard3_0169", "index": 169, "difficulty": "hard", "eq1_id": 1506, "eq2_id": 2816, "equation1": "x = (y * x) * (z * (z * x))", "equation2": "x = ((y * z) * (z * w)) * x", "answer": false}
|
| 170 |
+
{"id": "hard3_0170", "index": 170, "difficulty": "hard", "eq1_id": 1510, "eq2_id": 1163, "equation1": "x = (y * x) * (z * (w * x))", "equation2": "x = y * ((z * (y * x)) * x)", "answer": false}
|
| 171 |
+
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|
| 172 |
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{"id": "hard3_0172", "index": 172, "difficulty": "hard", "eq1_id": 1521, "eq2_id": 483, "equation1": "x = (y * y) * (x * (z * x))", "equation2": "x = y * (x * (z * (x * x)))", "answer": false}
|
| 173 |
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{"id": "hard3_0173", "index": 173, "difficulty": "hard", "eq1_id": 1539, "eq2_id": 524, "equation1": "x = (y * y) * (z * (y * x))", "equation2": "x = y * (y * (z * (y * x)))", "answer": false}
|
| 174 |
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{"id": "hard3_0174", "index": 174, "difficulty": "hard", "eq1_id": 1539, "eq2_id": 2521, "equation1": "x = (y * y) * (z * (y * x))", "equation2": "x = (y * ((x * z) * z)) * x", "answer": false}
|
| 175 |
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{"id": "hard3_0175", "index": 175, "difficulty": "hard", "eq1_id": 1560, "eq2_id": 4121, "equation1": "x = (y * z) * (x * (z * x))", "equation2": "x * y = ((x * x) * y) * y", "answer": false}
|
| 176 |
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{"id": "hard3_0176", "index": 176, "difficulty": "hard", "eq1_id": 1571, "eq2_id": 2541, "equation1": "x = (y * z) * (y * (x * z))", "equation2": "x = (y * ((y * y) * x)) * y", "answer": true}
|
| 177 |
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{"id": "hard3_0177", "index": 177, "difficulty": "hard", "eq1_id": 1573, "eq2_id": 3068, "equation1": "x = (y * z) * (y * (y * x))", "equation2": "x = (((x * y) * x) * y) * x", "answer": false}
|
| 178 |
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{"id": "hard3_0178", "index": 178, "difficulty": "hard", "eq1_id": 1573, "eq2_id": 4445, "equation1": "x = (y * z) * (y * (y * x))", "equation2": "x * (y * x) = (y * y) * x", "answer": false}
|
| 179 |
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{"id": "hard3_0179", "index": 179, "difficulty": "hard", "eq1_id": 1586, "eq2_id": 2571, "equation1": "x = (y * z) * (z * (x * x))", "equation2": "x = (y * ((z * x) * y)) * x", "answer": false}
|
| 180 |
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{"id": "hard3_0180", "index": 180, "difficulty": "hard", "eq1_id": 1594, "eq2_id": 2644, "equation1": "x = (y * z) * (z * (z * x))", "equation2": "x = ((x * x) * (x * x)) * x", "answer": false}
|
| 181 |
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{"id": "hard3_0181", "index": 181, "difficulty": "hard", "eq1_id": 1603, "eq2_id": 2733, "equation1": "x = (y * z) * (w * (x * x))", "equation2": "x = ((y * y) * (x * x)) * x", "answer": false}
|
| 182 |
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|
| 183 |
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{"id": "hard3_0183", "index": 183, "difficulty": "hard", "eq1_id": 1642, "eq2_id": 1432, "equation1": "x = (x * x) * ((y * z) * z)", "equation2": "x = (x * x) * (y * (x * y))", "answer": true}
|
| 184 |
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|
| 185 |
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|
| 186 |
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|
| 187 |
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|
| 188 |
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|
| 189 |
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|
| 190 |
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|
| 191 |
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|
| 192 |
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|
| 193 |
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|
| 194 |
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|
| 195 |
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|
| 196 |
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|
| 197 |
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|
| 198 |
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|
| 199 |
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|
| 200 |
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|
| 201 |
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|
| 202 |
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|
| 203 |
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|
| 204 |
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|
| 205 |
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|
| 206 |
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|
| 207 |
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|
| 208 |
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|
| 209 |
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{"id": "hard3_0209", "index": 209, "difficulty": "hard", "eq1_id": 1966, "eq2_id": 2207, "equation1": "x = (y * (z * x)) * (z * x)", "equation2": "x = ((y * z) * z) * (w * x)", "answer": true}
|
| 210 |
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{"id": "hard3_0210", "index": 210, "difficulty": "hard", "eq1_id": 1970, "eq2_id": 2063, "equation1": "x = (y * (z * x)) * (w * x)", "equation2": "x = ((x * y) * y) * (y * x)", "answer": true}
|
| 211 |
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|
| 212 |
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{"id": "hard3_0212", "index": 212, "difficulty": "hard", "eq1_id": 2004, "eq2_id": 104, "equation1": "x = (y * (z * z)) * (w * x)", "equation2": "x = x * ((y * x) * x)", "answer": true}
|
| 213 |
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{"id": "hard3_0213", "index": 213, "difficulty": "hard", "eq1_id": 2004, "eq2_id": 3883, "equation1": "x = (y * (z * z)) * (w * x)", "equation2": "x * x = (y * (x * z)) * x", "answer": true}
|
| 214 |
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{"id": "hard3_0214", "index": 214, "difficulty": "hard", "eq1_id": 2042, "eq2_id": 2692, "equation1": "x = ((x * x) * y) * (x * z)", "equation2": "x = ((x * y) * (z * w)) * y", "answer": true}
|
| 215 |
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{"id": "hard3_0215", "index": 215, "difficulty": "hard", "eq1_id": 2046, "eq2_id": 1063, "equation1": "x = ((x * x) * y) * (z * x)", "equation2": "x = x * ((y * (z * z)) * x)", "answer": false}
|
| 216 |
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{"id": "hard3_0216", "index": 216, "difficulty": "hard", "eq1_id": 2048, "eq2_id": 4512, "equation1": "x = ((x * x) * y) * (z * z)", "equation2": "x * (y * z) = (x * y) * z", "answer": false}
|
| 217 |
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{"id": "hard3_0217", "index": 217, "difficulty": "hard", "eq1_id": 2049, "eq2_id": 215, "equation1": "x = ((x * x) * y) * (z * w)", "equation2": "x = (x * (y * z)) * y", "answer": false}
|
| 218 |
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{"id": "hard3_0218", "index": 218, "difficulty": "hard", "eq1_id": 2059, "eq2_id": 462, "equation1": "x = ((x * y) * x) * (z * w)", "equation2": "x = x * (y * (z * (w * u)))", "answer": false}
|
| 219 |
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{"id": "hard3_0219", "index": 219, "difficulty": "hard", "eq1_id": 2059, "eq2_id": 3077, "equation1": "x = ((x * y) * x) * (z * w)", "equation2": "x = (((x * y) * y) * x) * z", "answer": false}
|
| 220 |
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{"id": "hard3_0220", "index": 220, "difficulty": "hard", "eq1_id": 2069, "eq2_id": 1635, "equation1": "x = ((x * y) * y) * (z * w)", "equation2": "x = (x * x) * ((y * x) * y)", "answer": false}
|
| 221 |
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{"id": "hard3_0221", "index": 221, "difficulty": "hard", "eq1_id": 2075, "eq2_id": 2872, "equation1": "x = ((x * y) * z) * (y * y)", "equation2": "x = ((x * (y * y)) * x) * x", "answer": true}
|
| 222 |
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{"id": "hard3_0222", "index": 222, "difficulty": "hard", "eq1_id": 2081, "eq2_id": 656, "equation1": "x = ((x * y) * z) * (z * w)", "equation2": "x = x * (y * ((z * y) * w))", "answer": false}
|
| 223 |
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{"id": "hard3_0223", "index": 223, "difficulty": "hard", "eq1_id": 2083, "eq2_id": 1647, "equation1": "x = ((x * y) * z) * (w * y)", "equation2": "x = (x * y) * ((x * y) * x)", "answer": false}
|
| 224 |
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{"id": "hard3_0224", "index": 224, "difficulty": "hard", "eq1_id": 2083, "eq2_id": 1833, "equation1": "x = ((x * y) * z) * (w * y)", "equation2": "x = (x * (x * x)) * (x * y)", "answer": false}
|
| 225 |
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{"id": "hard3_0225", "index": 225, "difficulty": "hard", "eq1_id": 2083, "eq2_id": 2243, "equation1": "x = ((x * y) * z) * (w * y)", "equation2": "x = (x * (x * (y * x))) * x", "answer": false}
|
| 226 |
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{"id": "hard3_0226", "index": 226, "difficulty": "hard", "eq1_id": 2084, "eq2_id": 1430, "equation1": "x = ((x * y) * z) * (w * z)", "equation2": "x = (x * x) * (x * (y * z))", "answer": false}
|
| 227 |
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{"id": "hard3_0227", "index": 227, "difficulty": "hard", "eq1_id": 2084, "eq2_id": 3095, "equation1": "x = ((x * y) * z) * (w * z)", "equation2": "x = (((x * y) * z) * z) * z", "answer": false}
|
| 228 |
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{"id": "hard3_0228", "index": 228, "difficulty": "hard", "eq1_id": 2086, "eq2_id": 56, "equation1": "x = ((x * y) * z) * (w * u)", "equation2": "x = x * (y * (y * y))", "answer": false}
|
| 229 |
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{"id": "hard3_0229", "index": 229, "difficulty": "hard", "eq1_id": 2093, "eq2_id": 1890, "equation1": "x = ((y * x) * x) * (z * x)", "equation2": "x = (y * (x * x)) * (z * x)", "answer": false}
|
| 230 |
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{"id": "hard3_0230", "index": 230, "difficulty": "hard", "eq1_id": 2103, "eq2_id": 4187, "equation1": "x = ((y * x) * y) * (z * x)", "equation2": "x * y = ((y * z) * w) * y", "answer": true}
|
| 231 |
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{"id": "hard3_0231", "index": 231, "difficulty": "hard", "eq1_id": 2105, "eq2_id": 2300, "equation1": "x = ((y * x) * y) * (z * z)", "equation2": "x = (y * (x * (y * x))) * x", "answer": true}
|
| 232 |
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{"id": "hard3_0232", "index": 232, "difficulty": "hard", "eq1_id": 2113, "eq2_id": 3537, "equation1": "x = ((y * x) * z) * (y * z)", "equation2": "x * y = x * ((z * z) * y)", "answer": true}
|
| 233 |
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{"id": "hard3_0233", "index": 233, "difficulty": "hard", "eq1_id": 2119, "eq2_id": 4655, "equation1": "x = ((y * x) * z) * (w * x)", "equation2": "(x * y) * y = (x * z) * y", "answer": true}
|
| 234 |
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{"id": "hard3_0234", "index": 234, "difficulty": "hard", "eq1_id": 2126, "eq2_id": 124, "equation1": "x = ((y * y) * x) * (x * z)", "equation2": "x = y * ((y * x) * x)", "answer": false}
|
| 235 |
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{"id": "hard3_0235", "index": 235, "difficulty": "hard", "eq1_id": 2126, "eq2_id": 1071, "equation1": "x = ((y * y) * x) * (x * z)", "equation2": "x = x * ((y * (z * w)) * u)", "answer": false}
|
| 236 |
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{"id": "hard3_0236", "index": 236, "difficulty": "hard", "eq1_id": 2126, "eq2_id": 1691, "equation1": "x = ((y * y) * x) * (x * z)", "equation2": "x = (y * x) * ((y * x) * x)", "answer": false}
|
| 237 |
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{"id": "hard3_0237", "index": 237, "difficulty": "hard", "eq1_id": 2126, "eq2_id": 3734, "equation1": "x = ((y * y) * x) * (x * z)", "equation2": "x * y = (x * z) * (x * w)", "answer": false}
|
| 238 |
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{"id": "hard3_0238", "index": 238, "difficulty": "hard", "eq1_id": 2144, "eq2_id": 1734, "equation1": "x = ((y * y) * z) * (x * x)", "equation2": "x = (y * y) * ((y * z) * x)", "answer": true}
|
| 239 |
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{"id": "hard3_0239", "index": 239, "difficulty": "hard", "eq1_id": 2156, "eq2_id": 1887, "equation1": "x = ((y * y) * z) * (w * x)", "equation2": "x = (y * (x * x)) * (y * x)", "answer": true}
|
| 240 |
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{"id": "hard3_0240", "index": 240, "difficulty": "hard", "eq1_id": 2156, "eq2_id": 2097, "equation1": "x = ((y * y) * z) * (w * x)", "equation2": "x = ((y * x) * y) * (x * x)", "answer": true}
|
| 241 |
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{"id": "hard3_0241", "index": 241, "difficulty": "hard", "eq1_id": 2164, "eq2_id": 1634, "equation1": "x = ((y * z) * x) * (x * w)", "equation2": "x = (x * x) * ((y * x) * x)", "answer": false}
|
| 242 |
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{"id": "hard3_0242", "index": 242, "difficulty": "hard", "eq1_id": 2164, "eq2_id": 2044, "equation1": "x = ((y * z) * x) * (x * w)", "equation2": "x = ((x * x) * y) * (y * y)", "answer": false}
|
| 243 |
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{"id": "hard3_0243", "index": 243, "difficulty": "hard", "eq1_id": 2173, "eq2_id": 2014, "equation1": "x = ((y * z) * x) * (w * x)", "equation2": "x = (y * (z * w)) * (y * x)", "answer": true}
|
| 244 |
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{"id": "hard3_0244", "index": 244, "difficulty": "hard", "eq1_id": 2190, "eq2_id": 3388, "equation1": "x = ((y * z) * y) * (w * x)", "equation2": "x * y = z * (x * (z * y))", "answer": true}
|
| 245 |
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{"id": "hard3_0245", "index": 245, "difficulty": "hard", "eq1_id": 2232, "eq2_id": 3261, "equation1": "x = ((y * z) * w) * (u * x)", "equation2": "x * x = x * (y * (y * x))", "answer": true}
|
| 246 |
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{"id": "hard3_0246", "index": 246, "difficulty": "hard", "eq1_id": 2248, "eq2_id": 3259, "equation1": "x = (x * (x * (y * y))) * z", "equation2": "x * x = x * (y * (x * y))", "answer": true}
|
| 247 |
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{"id": "hard3_0247", "index": 247, "difficulty": "hard", "eq1_id": 2255, "eq2_id": 2487, "equation1": "x = (x * (y * (x * x))) * z", "equation2": "x = (x * ((y * z) * z)) * w", "answer": true}
|
| 248 |
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{"id": "hard3_0248", "index": 248, "difficulty": "hard", "eq1_id": 2257, "eq2_id": 4583, "equation1": "x = (x * (y * (x * y))) * y", "equation2": "(x * x) * x = (x * x) * y", "answer": false}
|
| 249 |
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{"id": "hard3_0249", "index": 249, "difficulty": "hard", "eq1_id": 2262, "eq2_id": 1851, "equation1": "x = (x * (y * (x * z))) * w", "equation2": "x = (x * (y * x)) * (y * y)", "answer": true}
|
| 250 |
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{"id": "hard3_0250", "index": 250, "difficulty": "hard", "eq1_id": 2265, "eq2_id": 3337, "equation1": "x = (x * (y * (y * x))) * z", "equation2": "x * y = x * (z * (w * x))", "answer": true}
|
| 251 |
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{"id": "hard3_0251", "index": 251, "difficulty": "hard", "eq1_id": 2268, "eq2_id": 1851, "equation1": "x = (x * (y * (y * y))) * z", "equation2": "x = (x * (y * x)) * (y * y)", "answer": true}
|
| 252 |
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{"id": "hard3_0252", "index": 252, "difficulty": "hard", "eq1_id": 2268, "eq2_id": 1866, "equation1": "x = (x * (y * (y * y))) * z", "equation2": "x = (x * (y * y)) * (z * w)", "answer": true}
|
| 253 |
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|
| 254 |
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|
| 255 |
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|
| 256 |
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|
| 257 |
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|
| 258 |
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|
| 259 |
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|
| 260 |
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| 261 |
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| 262 |
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|
| 263 |
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|
| 264 |
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|
| 265 |
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| 266 |
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|
| 267 |
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| 268 |
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| 269 |
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| 270 |
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| 271 |
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| 272 |
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|
| 273 |
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|
| 274 |
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|
| 275 |
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|
| 276 |
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|
| 277 |
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|
| 278 |
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|
| 279 |
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|
| 280 |
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|
| 281 |
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|
| 282 |
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|
| 283 |
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|
| 284 |
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|
| 285 |
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|
| 286 |
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|
| 287 |
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|
| 288 |
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|
| 289 |
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|
| 290 |
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|
| 291 |
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|
| 292 |
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{"id": "hard3_0292", "index": 292, "difficulty": "hard", "eq1_id": 2757, "eq2_id": 835, "equation1": "x = ((y * y) * (z * y)) * x", "equation2": "x = x * ((y * x) * (y * x))", "answer": true}
|
| 293 |
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{"id": "hard3_0293", "index": 293, "difficulty": "hard", "eq1_id": 2787, "eq2_id": 466, "equation1": "x = ((y * z) * (y * x)) * x", "equation2": "x = y * (x * (x * (y * x)))", "answer": false}
|
| 294 |
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{"id": "hard3_0294", "index": 294, "difficulty": "hard", "eq1_id": 2787, "eq2_id": 3007, "equation1": "x = ((y * z) * (y * x)) * x", "equation2": "x = ((y * (z * z)) * x) * x", "answer": true}
|
| 295 |
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{"id": "hard3_0295", "index": 295, "difficulty": "hard", "eq1_id": 2816, "eq2_id": 1953, "equation1": "x = ((y * z) * (z * w)) * x", "equation2": "x = (y * (y * z)) * (w * x)", "answer": true}
|
| 296 |
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{"id": "hard3_0296", "index": 296, "difficulty": "hard", "eq1_id": 2816, "eq2_id": 3197, "equation1": "x = ((y * z) * (z * w)) * x", "equation2": "x = (((y * z) * y) * y) * x", "answer": true}
|
| 297 |
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{"id": "hard3_0297", "index": 297, "difficulty": "hard", "eq1_id": 2831, "eq2_id": 2060, "equation1": "x = ((y * z) * (w * z)) * x", "equation2": "x = ((x * y) * y) * (x * x)", "answer": true}
|
| 298 |
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{"id": "hard3_0298", "index": 298, "difficulty": "hard", "eq1_id": 2831, "eq2_id": 4385, "equation1": "x = ((y * z) * (w * z)) * x", "equation2": "x * (x * x) = (y * x) * x", "answer": true}
|
| 299 |
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{"id": "hard3_0299", "index": 299, "difficulty": "hard", "eq1_id": 2841, "eq2_id": 4275, "equation1": "x = ((y * z) * (w * u)) * x", "equation2": "x * (x * x) = y * (y * x)", "answer": true}
|
| 300 |
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{"id": "hard3_0300", "index": 300, "difficulty": "hard", "eq1_id": 2848, "eq2_id": 1063, "equation1": "x = ((x * (x * x)) * x) * y", "equation2": "x = x * ((y * (z * z)) * x)", "answer": false}
|
| 301 |
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{"id": "hard3_0301", "index": 301, "difficulty": "hard", "eq1_id": 2851, "eq2_id": 109, "equation1": "x = ((x * (x * x)) * y) * z", "equation2": "x = x * ((y * y) * z)", "answer": false}
|
| 302 |
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{"id": "hard3_0302", "index": 302, "difficulty": "hard", "eq1_id": 2852, "eq2_id": 2886, "equation1": "x = ((x * (x * y)) * x) * x", "equation2": "x = ((x * (y * z)) * y) * x", "answer": false}
|
| 303 |
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{"id": "hard3_0303", "index": 303, "difficulty": "hard", "eq1_id": 2856, "eq2_id": 616, "equation1": "x = ((x * (x * y)) * y) * y", "equation2": "x = x * (x * ((x * y) * x))", "answer": false}
|
| 304 |
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{"id": "hard3_0304", "index": 304, "difficulty": "hard", "eq1_id": 2859, "eq2_id": 1647, "equation1": "x = ((x * (x * y)) * z) * y", "equation2": "x = (x * y) * ((x * y) * x)", "answer": false}
|
| 305 |
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{"id": "hard3_0305", "index": 305, "difficulty": "hard", "eq1_id": 2864, "eq2_id": 624, "equation1": "x = ((x * (y * x)) * x) * z", "equation2": "x = x * (x * ((y * y) * z))", "answer": false}
|
| 306 |
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{"id": "hard3_0306", "index": 306, "difficulty": "hard", "eq1_id": 2871, "eq2_id": 855, "equation1": "x = ((x * (y * x)) * z) * w", "equation2": "x = x * ((y * z) * (x * w))", "answer": false}
|
| 307 |
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{"id": "hard3_0307", "index": 307, "difficulty": "hard", "eq1_id": 2874, "eq2_id": 2857, "equation1": "x = ((x * (y * y)) * x) * z", "equation2": "x = ((x * (x * y)) * y) * z", "answer": true}
|
| 308 |
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{"id": "hard3_0308", "index": 308, "difficulty": "hard", "eq1_id": 2884, "eq2_id": 2045, "equation1": "x = ((x * (y * z)) * x) * z", "equation2": "x = ((x * x) * y) * (y * z)", "answer": true}
|
| 309 |
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{"id": "hard3_0309", "index": 309, "difficulty": "hard", "eq1_id": 2887, "eq2_id": 3516, "equation1": "x = ((x * (y * z)) * y) * y", "equation2": "x * y = x * ((x * z) * z)", "answer": false}
|
| 310 |
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{"id": "hard3_0310", "index": 310, "difficulty": "hard", "eq1_id": 2889, "eq2_id": 27, "equation1": "x = ((x * (y * z)) * y) * w", "equation2": "x = (x * y) * z", "answer": false}
|
| 311 |
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{"id": "hard3_0311", "index": 311, "difficulty": "hard", "eq1_id": 2892, "eq2_id": 4119, "equation1": "x = ((x * (y * z)) * z) * z", "equation2": "x * y = ((x * x) * x) * z", "answer": false}
|
| 312 |
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{"id": "hard3_0312", "index": 312, "difficulty": "hard", "eq1_id": 2896, "eq2_id": 55, "equation1": "x = ((x * (y * z)) * w) * z", "equation2": "x = x * (y * (y * x))", "answer": false}
|
| 313 |
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{"id": "hard3_0313", "index": 313, "difficulty": "hard", "eq1_id": 2905, "eq2_id": 4564, "equation1": "x = ((y * (x * x)) * z) * x", "equation2": "x * (y * z) = (w * y) * z", "answer": true}
|
| 314 |
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{"id": "hard3_0314", "index": 314, "difficulty": "hard", "eq1_id": 2923, "eq2_id": 1623, "equation1": "x = ((y * (x * z)) * y) * x", "equation2": "x = (y * z) * (w * (u * x))", "answer": true}
|
| 315 |
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{"id": "hard3_0315", "index": 315, "difficulty": "hard", "eq1_id": 2927, "eq2_id": 765, "equation1": "x = ((y * (x * z)) * z) * x", "equation2": "x = y * (z * ((y * z) * x))", "answer": true}
|
| 316 |
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{"id": "hard3_0316", "index": 316, "difficulty": "hard", "eq1_id": 2927, "eq2_id": 3890, "equation1": "x = ((y * (x * z)) * z) * x", "equation2": "x * x = (y * (y * y)) * x", "answer": true}
|
| 317 |
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{"id": "hard3_0317", "index": 317, "difficulty": "hard", "eq1_id": 2927, "eq2_id": 4611, "equation1": "x = ((y * (x * z)) * z) * x", "equation2": "(x * x) * y = (y * z) * y", "answer": true}
|
| 318 |
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{"id": "hard3_0318", "index": 318, "difficulty": "hard", "eq1_id": 2931, "eq2_id": 2484, "equation1": "x = ((y * (x * z)) * w) * x", "equation2": "x = (x * ((y * z) * z)) * x", "answer": true}
|
| 319 |
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{"id": "hard3_0319", "index": 319, "difficulty": "hard", "eq1_id": 2931, "eq2_id": 4498, "equation1": "x = ((y * (x * z)) * w) * x", "equation2": "x * (y * y) = (z * z) * y", "answer": true}
|
| 320 |
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{"id": "hard3_0320", "index": 320, "difficulty": "hard", "eq1_id": 2973, "eq2_id": 4124, "equation1": "x = ((y * (z * x)) * x) * x", "equation2": "x * y = ((x * x) * z) * y", "answer": false}
|
| 321 |
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{"id": "hard3_0321", "index": 321, "difficulty": "hard", "eq1_id": 2985, "eq2_id": 1374, "equation1": "x = ((y * (z * x)) * w) * x", "equation2": "x = y * (((z * y) * z) * x)", "answer": true}
|
| 322 |
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{"id": "hard3_0322", "index": 322, "difficulty": "hard", "eq1_id": 2998, "eq2_id": 3870, "equation1": "x = ((y * (z * y)) * z) * x", "equation2": "x * x = (x * (y * y)) * x", "answer": false}
|
| 323 |
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{"id": "hard3_0323", "index": 323, "difficulty": "hard", "eq1_id": 3034, "eq2_id": 419, "equation1": "x = ((y * (z * w)) * z) * x", "equation2": "x = x * (x * (y * (y * x)))", "answer": true}
|
| 324 |
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{"id": "hard3_0324", "index": 324, "difficulty": "hard", "eq1_id": 3034, "eq2_id": 1228, "equation1": "x = ((y * (z * w)) * z) * x", "equation2": "x = x * (((x * y) * x) * x)", "answer": true}
|
| 325 |
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{"id": "hard3_0325", "index": 325, "difficulty": "hard", "eq1_id": 3034, "eq2_id": 3762, "equation1": "x = ((y * (z * w)) * z) * x", "equation2": "x * y = (y * y) * (y * y)", "answer": true}
|
| 326 |
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{"id": "hard3_0326", "index": 326, "difficulty": "hard", "eq1_id": 3039, "eq2_id": 3065, "equation1": "x = ((y * (z * w)) * w) * x", "equation2": "x = (((x * y) * x) * x) * x", "answer": true}
|
| 327 |
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{"id": "hard3_0327", "index": 327, "difficulty": "hard", "eq1_id": 3062, "eq2_id": 1462, "equation1": "x = (((x * x) * y) * z) * y", "equation2": "x = (x * y) * (z * (x * y))", "answer": false}
|
| 328 |
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{"id": "hard3_0328", "index": 328, "difficulty": "hard", "eq1_id": 3069, "eq2_id": 153, "equation1": "x = (((x * y) * x) * y) * y", "equation2": "x = (x * x) * (y * x)", "answer": false}
|
| 329 |
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{"id": "hard3_0329", "index": 329, "difficulty": "hard", "eq1_id": 3074, "eq2_id": 4288, "equation1": "x = (((x * y) * x) * z) * w", "equation2": "x * (x * y) = x * (z * z)", "answer": true}
|
| 330 |
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{"id": "hard3_0330", "index": 330, "difficulty": "hard", "eq1_id": 3086, "eq2_id": 2262, "equation1": "x = (((x * y) * z) * x) * y", "equation2": "x = (x * (y * (x * z))) * w", "answer": false}
|
| 331 |
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{"id": "hard3_0331", "index": 331, "difficulty": "hard", "eq1_id": 3092, "eq2_id": 3081, "equation1": "x = (((x * y) * z) * y) * w", "equation2": "x = (((x * y) * y) * z) * x", "answer": true}
|
| 332 |
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{"id": "hard3_0332", "index": 332, "difficulty": "hard", "eq1_id": 3095, "eq2_id": 2465, "equation1": "x = (((x * y) * z) * z) * z", "equation2": "x = (x * ((y * x) * z)) * w", "answer": false}
|
| 333 |
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{"id": "hard3_0333", "index": 333, "difficulty": "hard", "eq1_id": 3118, "eq2_id": 4525, "equation1": "x = (((y * x) * y) * z) * x", "equation2": "x * (y * z) = (y * x) * z", "answer": true}
|
| 334 |
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{"id": "hard3_0334", "index": 334, "difficulty": "hard", "eq1_id": 3130, "eq2_id": 231, "equation1": "x = (((y * x) * z) * z) * x", "equation2": "x = (y * (y * y)) * x", "answer": true}
|
| 335 |
+
{"id": "hard3_0335", "index": 335, "difficulty": "hard", "eq1_id": 3130, "eq2_id": 2119, "equation1": "x = (((y * x) * z) * z) * x", "equation2": "x = ((y * x) * z) * (w * x)", "answer": true}
|
| 336 |
+
{"id": "hard3_0336", "index": 336, "difficulty": "hard", "eq1_id": 3171, "eq2_id": 99, "equation1": "x = (((y * y) * z) * w) * x", "equation2": "x = x * ((x * x) * x)", "answer": true}
|
| 337 |
+
{"id": "hard3_0337", "index": 337, "difficulty": "hard", "eq1_id": 3171, "eq2_id": 3667, "equation1": "x = (((y * y) * z) * w) * x", "equation2": "x * x = (x * y) * (y * x)", "answer": true}
|
| 338 |
+
{"id": "hard3_0338", "index": 338, "difficulty": "hard", "eq1_id": 3171, "eq2_id": 4480, "equation1": "x = (((y * y) * z) * w) * x", "equation2": "x * (y * y) = (y * x) * y", "answer": true}
|
| 339 |
+
{"id": "hard3_0339", "index": 339, "difficulty": "hard", "eq1_id": 3193, "eq2_id": 2799, "equation1": "x = (((y * z) * y) * x) * x", "equation2": "x = ((y * z) * (y * w)) * x", "answer": false}
|
| 340 |
+
{"id": "hard3_0340", "index": 340, "difficulty": "hard", "eq1_id": 3247, "eq2_id": 276, "equation1": "x = (((y * z) * w) * u) * x", "equation2": "x = ((y * x) * z) * x", "answer": true}
|
| 341 |
+
{"id": "hard3_0341", "index": 341, "difficulty": "hard", "eq1_id": 3247, "eq2_id": 2389, "equation1": "x = (((y * z) * w) * u) * x", "equation2": "x = (y * (z * (y * z))) * x", "answer": true}
|
| 342 |
+
{"id": "hard3_0342", "index": 342, "difficulty": "hard", "eq1_id": 3270, "eq2_id": 3736, "equation1": "x * x = y * (x * (x * z))", "equation2": "x * y = (x * z) * (y * y)", "answer": false}
|
| 343 |
+
{"id": "hard3_0343", "index": 343, "difficulty": "hard", "eq1_id": 3270, "eq2_id": 4093, "equation1": "x * x = y * (x * (x * z))", "equation2": "x * x = ((y * y) * y) * x", "answer": false}
|
| 344 |
+
{"id": "hard3_0344", "index": 344, "difficulty": "hard", "eq1_id": 3273, "eq2_id": 4312, "equation1": "x * x = y * (x * (y * z))", "equation2": "x * (x * y) = z * (w * w)", "answer": false}
|
| 345 |
+
{"id": "hard3_0345", "index": 345, "difficulty": "hard", "eq1_id": 3277, "eq2_id": 4314, "equation1": "x * x = y * (x * (z * w))", "equation2": "x * (y * x) = x * (y * y)", "answer": false}
|
| 346 |
+
{"id": "hard3_0346", "index": 346, "difficulty": "hard", "eq1_id": 3277, "eq2_id": 4365, "equation1": "x * x = y * (x * (z * w))", "equation2": "x * (y * z) = y * (z * w)", "answer": false}
|
| 347 |
+
{"id": "hard3_0347", "index": 347, "difficulty": "hard", "eq1_id": 3277, "eq2_id": 4440, "equation1": "x * x = y * (x * (z * w))", "equation2": "x * (y * x) = (x * z) * z", "answer": false}
|
| 348 |
+
{"id": "hard3_0348", "index": 348, "difficulty": "hard", "eq1_id": 3280, "eq2_id": 3777, "equation1": "x * x = y * (y * (x * z))", "equation2": "x * y = (y * z) * (z * y)", "answer": false}
|
| 349 |
+
{"id": "hard3_0349", "index": 349, "difficulty": "hard", "eq1_id": 3283, "eq2_id": 4316, "equation1": "x * x = y * (y * (y * z))", "equation2": "x * (y * x) = x * (z * x)", "answer": false}
|
| 350 |
+
{"id": "hard3_0350", "index": 350, "difficulty": "hard", "eq1_id": 3291, "eq2_id": 4480, "equation1": "x * x = y * (z * (x * w))", "equation2": "x * (y * y) = (y * x) * y", "answer": false}
|
| 351 |
+
{"id": "hard3_0351", "index": 351, "difficulty": "hard", "eq1_id": 3321, "eq2_id": 3535, "equation1": "x * y = x * (y * (z * x))", "equation2": "x * y = x * ((z * y) * w)", "answer": false}
|
| 352 |
+
{"id": "hard3_0352", "index": 352, "difficulty": "hard", "eq1_id": 3328, "eq2_id": 3313, "equation1": "x * y = x * (z * (x * w))", "equation2": "x * y = x * (x * (z * z))", "answer": true}
|
| 353 |
+
{"id": "hard3_0353", "index": 353, "difficulty": "hard", "eq1_id": 3349, "eq2_id": 4682, "equation1": "x * y = y * (x * (z * y))", "equation2": "(x * y) * z = (y * w) * z", "answer": true}
|
| 354 |
+
{"id": "hard3_0354", "index": 354, "difficulty": "hard", "eq1_id": 3360, "eq2_id": 379, "equation1": "x * y = y * (y * (z * z))", "equation2": "x * y = (x * y) * z", "answer": true}
|
| 355 |
+
{"id": "hard3_0355", "index": 355, "difficulty": "hard", "eq1_id": 3360, "eq2_id": 3505, "equation1": "x * y = y * (y * (z * z))", "equation2": "x * x = y * ((z * w) * z)", "answer": true}
|
| 356 |
+
{"id": "hard3_0356", "index": 356, "difficulty": "hard", "eq1_id": 3380, "eq2_id": 4171, "equation1": "x * y = z * (x * (x * y))", "equation2": "x * y = ((y * y) * z) * y", "answer": false}
|
| 357 |
+
{"id": "hard3_0357", "index": 357, "difficulty": "hard", "eq1_id": 3417, "eq2_id": 3737, "equation1": "x * y = z * (z * (y * x))", "equation2": "x * y = (x * z) * (y * z)", "answer": false}
|
| 358 |
+
{"id": "hard3_0358", "index": 358, "difficulty": "hard", "eq1_id": 3476, "eq2_id": 4470, "equation1": "x * x = y * ((x * y) * z)", "equation2": "x * (y * y) = (x * x) * y", "answer": false}
|
| 359 |
+
{"id": "hard3_0359", "index": 359, "difficulty": "hard", "eq1_id": 3483, "eq2_id": 3766, "equation1": "x * x = y * ((y * x) * z)", "equation2": "x * y = (y * y) * (z * z)", "answer": false}
|
| 360 |
+
{"id": "hard3_0360", "index": 360, "difficulty": "hard", "eq1_id": 3490, "eq2_id": 355, "equation1": "x * x = y * ((y * z) * w)", "equation2": "x * y = z * (w * y)", "answer": false}
|
| 361 |
+
{"id": "hard3_0361", "index": 361, "difficulty": "hard", "eq1_id": 3490, "eq2_id": 3471, "equation1": "x * x = y * ((y * z) * w)", "equation2": "x * x = y * ((x * x) * x)", "answer": true}
|
| 362 |
+
{"id": "hard3_0362", "index": 362, "difficulty": "hard", "eq1_id": 3499, "eq2_id": 3441, "equation1": "x * x = y * ((z * z) * x)", "equation2": "x * y = z * (w * (z * y))", "answer": false}
|
| 363 |
+
{"id": "hard3_0363", "index": 363, "difficulty": "hard", "eq1_id": 3502, "eq2_id": 4109, "equation1": "x * x = y * ((z * z) * w)", "equation2": "x * x = ((y * z) * z) * y", "answer": false}
|
| 364 |
+
{"id": "hard3_0364", "index": 364, "difficulty": "hard", "eq1_id": 3514, "eq2_id": 4318, "equation1": "x * y = x * ((x * z) * x)", "equation2": "x * (y * x) = x * (z * z)", "answer": true}
|
| 365 |
+
{"id": "hard3_0365", "index": 365, "difficulty": "hard", "eq1_id": 3536, "eq2_id": 326, "equation1": "x * y = x * ((z * z) * x)", "equation2": "x * y = x * (y * y)", "answer": true}
|
| 366 |
+
{"id": "hard3_0366", "index": 366, "difficulty": "hard", "eq1_id": 3621, "eq2_id": 3471, "equation1": "x * y = z * ((z * y) * y)", "equation2": "x * x = y * ((x * x) * x)", "answer": true}
|
| 367 |
+
{"id": "hard3_0367", "index": 367, "difficulty": "hard", "eq1_id": 3629, "eq2_id": 4204, "equation1": "x * y = z * ((z * w) * y)", "equation2": "x * y = ((z * x) * w) * y", "answer": true}
|
| 368 |
+
{"id": "hard3_0368", "index": 368, "difficulty": "hard", "eq1_id": 3669, "eq2_id": 3333, "equation1": "x * x = (x * y) * (y * z)", "equation2": "x * y = x * (z * (z * x))", "answer": false}
|
| 369 |
+
{"id": "hard3_0369", "index": 369, "difficulty": "hard", "eq1_id": 3676, "eq2_id": 4682, "equation1": "x * x = (y * x) * (x * z)", "equation2": "(x * y) * z = (y * w) * z", "answer": false}
|
| 370 |
+
{"id": "hard3_0370", "index": 370, "difficulty": "hard", "eq1_id": 3683, "eq2_id": 3593, "equation1": "x * x = (y * x) * (z * w)", "equation2": "x * y = z * ((x * z) * w)", "answer": false}
|
| 371 |
+
{"id": "hard3_0371", "index": 371, "difficulty": "hard", "eq1_id": 3705, "eq2_id": 4362, "equation1": "x * x = (y * z) * (z * w)", "equation2": "x * (y * z) = y * (x * z)", "answer": false}
|
| 372 |
+
{"id": "hard3_0372", "index": 372, "difficulty": "hard", "eq1_id": 3728, "eq2_id": 4508, "equation1": "x * y = (x * y) * (z * y)", "equation2": "x * (y * z) = (x * x) * z", "answer": false}
|
| 373 |
+
{"id": "hard3_0373", "index": 373, "difficulty": "hard", "eq1_id": 3730, "eq2_id": 3265, "equation1": "x * y = (x * y) * (z * w)", "equation2": "x * x = x * (y * (z * y))", "answer": false}
|
| 374 |
+
{"id": "hard3_0374", "index": 374, "difficulty": "hard", "eq1_id": 3745, "eq2_id": 377, "equation1": "x * y = (x * z) * (w * z)", "equation2": "x * y = (x * y) * x", "answer": true}
|
| 375 |
+
{"id": "hard3_0375", "index": 375, "difficulty": "hard", "eq1_id": 3773, "eq2_id": 4134, "equation1": "x * y = (y * z) * (y * y)", "equation2": "x * y = ((x * y) * z) * y", "answer": true}
|
| 376 |
+
{"id": "hard3_0376", "index": 376, "difficulty": "hard", "eq1_id": 3791, "eq2_id": 4283, "equation1": "x * y = (z * x) * (y * z)", "equation2": "x * (x * y) = x * (y * x)", "answer": true}
|
| 377 |
+
{"id": "hard3_0377", "index": 377, "difficulty": "hard", "eq1_id": 3798, "eq2_id": 399, "equation1": "x * y = (z * x) * (w * y)", "equation2": "x * y = (z * y) * y", "answer": false}
|
| 378 |
+
{"id": "hard3_0378", "index": 378, "difficulty": "hard", "eq1_id": 3811, "eq2_id": 3852, "equation1": "x * y = (z * y) * (z * y)", "equation2": "x * y = (z * w) * (w * y)", "answer": true}
|
| 379 |
+
{"id": "hard3_0379", "index": 379, "difficulty": "hard", "eq1_id": 3857, "eq2_id": 4316, "equation1": "x * y = (z * w) * (u * y)", "equation2": "x * (y * x) = x * (z * x)", "answer": true}
|
| 380 |
+
{"id": "hard3_0380", "index": 380, "difficulty": "hard", "eq1_id": 3889, "eq2_id": 4270, "equation1": "x * x = (y * (y * x)) * z", "equation2": "x * (x * x) = x * (y * y)", "answer": true}
|
| 381 |
+
{"id": "hard3_0381", "index": 381, "difficulty": "hard", "eq1_id": 3941, "eq2_id": 3936, "equation1": "x * y = (x * (z * y)) * w", "equation2": "x * y = (x * (z * x)) * z", "answer": true}
|
| 382 |
+
{"id": "hard3_0382", "index": 382, "difficulty": "hard", "eq1_id": 3946, "eq2_id": 4339, "equation1": "x * y = (x * (z * w)) * x", "equation2": "x * (y * y) = x * (y * z)", "answer": true}
|
| 383 |
+
{"id": "hard3_0383", "index": 383, "difficulty": "hard", "eq1_id": 3972, "eq2_id": 4168, "equation1": "x * y = (y * (z * x)) * y", "equation2": "x * y = ((y * y) * y) * y", "answer": false}
|
| 384 |
+
{"id": "hard3_0384", "index": 384, "difficulty": "hard", "eq1_id": 4088, "eq2_id": 3700, "equation1": "x * x = ((y * x) * z) * z", "equation2": "x * x = (y * z) * (y * z)", "answer": true}
|
| 385 |
+
{"id": "hard3_0385", "index": 385, "difficulty": "hard", "eq1_id": 4099, "eq2_id": 359, "equation1": "x * x = ((y * y) * z) * w", "equation2": "x * x = (x * x) * x", "answer": true}
|
| 386 |
+
{"id": "hard3_0386", "index": 386, "difficulty": "hard", "eq1_id": 4110, "eq2_id": 359, "equation1": "x * x = ((y * z) * z) * z", "equation2": "x * x = (x * x) * x", "answer": true}
|
| 387 |
+
{"id": "hard3_0387", "index": 387, "difficulty": "hard", "eq1_id": 4140, "eq2_id": 4135, "equation1": "x * y = ((x * z) * x) * w", "equation2": "x * y = ((x * y) * z) * z", "answer": true}
|
| 388 |
+
{"id": "hard3_0388", "index": 388, "difficulty": "hard", "eq1_id": 4204, "eq2_id": 395, "equation1": "x * y = ((z * x) * w) * y", "equation2": "x * y = (z * x) * y", "answer": true}
|
| 389 |
+
{"id": "hard3_0389", "index": 389, "difficulty": "hard", "eq1_id": 4217, "eq2_id": 4362, "equation1": "x * y = ((z * y) * z) * y", "equation2": "x * (y * z) = y * (x * z)", "answer": true}
|
| 390 |
+
{"id": "hard3_0390", "index": 390, "difficulty": "hard", "eq1_id": 4221, "eq2_id": 4150, "equation1": "x * y = ((z * y) * w) * y", "equation2": "x * y = ((x * z) * w) * y", "answer": true}
|
| 391 |
+
{"id": "hard3_0391", "index": 391, "difficulty": "hard", "eq1_id": 4392, "eq2_id": 4677, "equation1": "x * (x * x) = (y * z) * y", "equation2": "(x * y) * z = (y * x) * z", "answer": false}
|
| 392 |
+
{"id": "hard3_0392", "index": 392, "difficulty": "hard", "eq1_id": 4404, "eq2_id": 4433, "equation1": "x * (x * y) = (x * z) * w", "equation2": "x * (y * x) = (x * x) * y", "answer": false}
|
| 393 |
+
{"id": "hard3_0393", "index": 393, "difficulty": "hard", "eq1_id": 4414, "eq2_id": 4623, "equation1": "x * (x * y) = (y * z) * w", "equation2": "(x * x) * y = (z * z) * w", "answer": true}
|
| 394 |
+
{"id": "hard3_0394", "index": 394, "difficulty": "hard", "eq1_id": 4527, "eq2_id": 3439, "equation1": "x * (y * z) = (y * y) * x", "equation2": "x * y = z * (w * (y * u))", "answer": false}
|
| 395 |
+
{"id": "hard3_0395", "index": 395, "difficulty": "hard", "eq1_id": 4545, "eq2_id": 4279, "equation1": "x * (y * z) = (z * y) * y", "equation2": "x * (x * x) = y * (z * y)", "answer": true}
|
| 396 |
+
{"id": "hard3_0396", "index": 396, "difficulty": "hard", "eq1_id": 4558, "eq2_id": 4519, "equation1": "x * (y * z) = (w * x) * y", "equation2": "x * (y * z) = (x * w) * y", "answer": true}
|
| 397 |
+
{"id": "hard3_0397", "index": 397, "difficulty": "hard", "eq1_id": 4573, "eq2_id": 4306, "equation1": "x * (y * z) = (w * w) * y", "equation2": "x * (x * y) = z * (y * w)", "answer": true}
|
| 398 |
+
{"id": "hard3_0398", "index": 398, "difficulty": "hard", "eq1_id": 4573, "eq2_id": 4343, "equation1": "x * (y * z) = (w * w) * y", "equation2": "x * (y * y) = y * (x * x)", "answer": true}
|
| 399 |
+
{"id": "hard3_0399", "index": 399, "difficulty": "hard", "eq1_id": 4577, "eq2_id": 4625, "equation1": "x * (y * z) = (w * u) * x", "equation2": "(x * x) * y = (z * w) * y", "answer": true}
|
| 400 |
+
{"id": "hard3_0400", "index": 400, "difficulty": "hard", "eq1_id": 4579, "eq2_id": 4631, "equation1": "x * (y * z) = (w * u) * z", "equation2": "(x * y) * x = (x * z) * x", "answer": true}
|
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metadata/hard3.json
ADDED
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| 1 |
+
{
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| 2 |
+
"subset_name": "hard3",
|
| 3 |
+
"source": "official",
|
| 4 |
+
"curators": [],
|
| 5 |
+
"difficulty": "hard",
|
| 6 |
+
"problem_count": 400,
|
| 7 |
+
"true_count": 195,
|
| 8 |
+
"false_count": 205,
|
| 9 |
+
"selection_method": "human_ai",
|
| 10 |
+
"derived_from": null,
|
| 11 |
+
"notes": ""
|
| 12 |
+
}
|