corbanyax/Countdown-3-Hash-Splits

Countdown-3 Puzzles with Hash-Defined Splits

Countdown-3 arithmetic puzzles for RL post-training with verifiable rewards: given three integers in [1, 50] and a target, write an expression that uses every number exactly once with + - * / and parentheses and equals the target. The universe is enumerated exhaustively with exact rational arithmetic (no sampling), and splits are defined by SHA-256 of the number multiset, so held-out splits use number combinations never seen in training. Used to train and evaluate Dress Rehearsal and the KV-cache precision study.

Splits

Split	Rows	Content
pool	102,497	training pool: every reachable integer target in [10, 100] for the remaining multisets
dev	500	first 500 multisets in hash order, one instance each
dev200	200	the first 200 problems of dev, the evaluation set used throughout the paper
test_id	1,000	next 1,000 multisets; evaluated once, for final policies only
test_ood_target	1,000	next 1,000 multisets with targets in [101, 200]
test_ood_4	1,000	4 numbers in [1, 25], targets in [10, 100]

Columns: prompt_id (e.g. cd3:1-1-31=29), numbers (list of int), target (int), n_numbers (int), split.

from datasets import load_dataset
ds = load_dataset("corbanyax/Countdown-3-Hash-Splits")          # all splits
dev200 = load_dataset("corbanyax/Countdown-3-Hash-Splits", split="dev200")

Construction

3-number multisets (22,100) are ordered by SHA-256 of cd3:a-b-c. The first 500 form dev, the next 1,000 test_id, the next 1,000 test_ood_target; each contributes exactly one instance, the reachable target whose instance key has the smallest SHA-256. All remaining multisets form pool. 4-number multisets are ordered the same way and the first 1,000 form test_ood_4. Reachable values come from exact rational arithmetic over every split into two sub-multisets; unary minus is not allowed. Rebuilding gives byte-identical files (SHA-256 of countdown_3.parquet recorded in the project log).

Prompt and reward

System: You are a careful assistant that solves arithmetic puzzles. User: Using the numbers {numbers}, create an arithmetic expression that equals {target}. Use every number exactly once. You may use +, -, *, / and parentheses. Show brief reasoning. End with the expression alone between answer tags, for example <answer>(100 - 75) * 60</answer>. The format example uses numbers above 50, so it never matches an instance. Reward 1 if the <answer> expression uses each number exactly once and evaluates exactly to the target, else 0; no format credit.

The original per-file layout is kept under raw/ (countdown_3.parquet, countdown_4.parquet).

Project family

Item	Hugging Face	Kaggle mirror
Dress Rehearsal adapters (this method)	corbanyax/Dress-Rehearsal-Qwen3-0.6B-4bit-KV-LoRA	model
KV-cache precision study adapters (33 runs)	corbanyax/KV-Cache-Precision-GRPO-Qwen3-0.6B-LoRA	model
Countdown-3 puzzles with hash-defined splits	corbanyax/Countdown-3-Hash-Splits	dataset
Full run logs, diagnostics, decision log	corbanyax/KV-Cache-Precision-GRPO-Run-Logs	dataset

Paper: Beyond a Single Score: A Multi-Objective Evaluation of KV-Cache Quantization in GRPO Training (under double-blind review, AAAI-27 Workshop on Multi-Objective and Multi-Task Optimization for Robust AI). All items are private until the review period ends.