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arc-barc-processed-direct-max4k-geminilitesols-test-valid

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You will be given some number of paired example inputs and outputs grids. The outputs were produced by applying a transformation rule to the input grids. In addition to the paired example inputs and outputs, there is also one test input without a known output. The inputs and outputs are each “grids”. A grid is a rectan...
[ "The transformation rule appears to construct a grid $O$ of size $L \\times L$, where $L$ is the length of the input row $I$. The center of the structure is determined by $R_c = (L-1)/2$ and $C_c$, the index of the unique non-zero color (which must be '2' based on examples) in the input $I$.\n\nThe value $O[R, C]$ ...
[{"input": [[0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0], [0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0], [2, 0, 0,...
[{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 1, 0, ...
arc 1
``` 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 2 0 1 0 0 0 1 0 0 0 2 0 0 0 0 0 2 0 0 0 1 0 0 0 1 0 0 0 2 0 0 0 2 0 1 0 0 0 1 0 0 0 1 0 0 0 2 0 2 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 2 0 1 0 0 0 ...
836
127.25
0.559689
0
3,948.625
[ 64, 32, 71, 53, 140, 60, 88, 95, 289, 49, 130, 61, 289, 289, 289, 37 ]
[ 0.7785467128027682, 0.889273356401384, 0.754325259515571, 0.8166089965397924, 0.5155709342560554, 0.7923875432525952, 0.6955017301038062, 0.671280276816609, 0, 0.8304498269896193, 0.5501730103806228, 0.7889273356401384, 0, 0, 0, 0.8719723183391004 ]
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
[ 2024, 1788, 4974, 3531, 3804, 5081, 2532, 1909, 6264, 3246, 3400, 1751, 8155, 3036, 8329, 3354 ]
[ [ [ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0,...
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["The transformation rule observed involves identifying the background color, extracting the most st(...TRUNCATED)
"[{\"input\": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7], [8, 8, 8, 8, 8, 8, 8, 8(...TRUNCATED)
"[{\"input\": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4(...TRUNCATED)
arc 2
"```\n4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\n4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4(...TRUNCATED)
2,961
468.25
0.307322
0
4,832.4375
[ 676, 676, 676, 184, 254, 676, 310, 302, 676, 202, 676, 676, 244, 292, 676, 296 ]
[0.0,0.0,0.0,0.727810650887574,0.6242603550295858,0.0,0.5414201183431953,0.5532544378698225,0.0,0.70(...TRUNCATED)
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
[ 2577, 5914, 7889, 6267, 3994, 4390, 5208, 2079, 2497, 3210, 2328, 7887, 6075, 6797, 5341, 4866 ]
[null,null,null,[[4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4],[4,4,4,4,4,4,4,4,4,4,4,4,4,4,(...TRUNCATED)
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["This problem requires identifying a structural mapping rule based on four major components present(...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 2, 0, 0(...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0(...TRUNCATED)
arc 2
"```\n3 3 3 3 3 3 3 3 3 3 6 6\n3 3 3 3 3 3 3 3 3 3 6 6\n3 3 3 3 6 6 6 6 3 3 6 6\n3 3 3 3 6 6 6 6 3 3(...TRUNCATED)
3,529
144
0
0
3,406.3125
[ 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144 ]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
[ 2958, 2076, 3207, 6895, 2091, 3473, 3954, 1718, 2052, 2432, 3674, 1976, 8088, 4644, 1595, 3668 ]
[[[3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6],[3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6],[3,3,3,3,3,3,3,3,6,6,6,6,6,6,6(...TRUNCATED)
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["This transformation involves three steps:\n1. **Object Segmentation:** Identify connected compone(...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0(...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0(...TRUNCATED)
barc_heavy
"```\n4 0 0 0 0 9 0 0 0 0 0 0 0 0\n4 0 0 0 0 9 0 0 0 0 0 0 0 0\n4 0 0 0 0 9 0 0 0 0 0 0 0 0\n4 0 0 0(...TRUNCATED)
3,030
140.3125
0.28412
0
4,702.75
[ 60, 196, 196, 196, 196, 59, 73, 196, 47, 196, 196, 196, 135, 196, 47, 60 ]
[0.6938775510204082,0.0,0.0,0.0,0.0,0.6989795918367347,0.6275510204081632,0.0,0.7602040816326531,0.0(...TRUNCATED)
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
[ 3989, 7934, 5392, 2813, 5447, 2665, 5729, 2573, 2944, 4842, 7832, 7855, 5494, 4443, 2042, 3250 ]
[[[4,0,0,0,0,0,9,0,0,0,0,0,0,0],[4,0,4,0,0,0,9,0,9,0,0,0,0,0],[0,4,4,4,0,0,0,9,9,9,0,0,0,0],[4,4,4,4(...TRUNCATED)
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["The transformation rule involves identifying the primary shape defined by the non-zero elements in(...TRUNCATED)
"[{\"input\": [[1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0,(...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3(...TRUNCATED)
arc 1
"```\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0 0 3 0 0 0 0\n0 0 1 1 0 0 0 0 0 0 0 3 3 0 (...TRUNCATED)
3,047
64.5625
0.711775
0
4,500.6875
[ 27, 23, 23, 20, 36, 36, 24, 36, 28, 224, 224, 28, 21, 33, 224, 26 ]
[0.8794642857142857,0.8973214285714286,0.8973214285714286,0.9107142857142857,0.8392857142857143,0.83(...TRUNCATED)
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
[ 7278, 4526, 2504, 6046, 1653, 4486, 5002, 3015, 3465, 7981, 7866, 2567, 3717, 3110, 4808, 3987 ]
[[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0,0,3,3,0,0,0],[0,0,1,1,0,0,0,0,0,0,0,3,3,3,0(...TRUNCATED)
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["The transformation rule identified from the examples is to extract all unique non-zero colors pres(...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 8], [0, 9, 9, 0, 7, 0, 7, 7, 0, 7, 0, 0], [0, 9, 9,(...TRUNCATED)
"[{\"input\": [[0, 6, 0, 9, 0, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 6, 0, 0], [5, 5, 5, 0, 0, 0, 0, 0, 6](...TRUNCATED)
barc_heavy
``` 6 9 5 4 2 8 ```
948
0.375
0.9375
0.875
485.5625
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3 ]
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.5, 1, 1, 1, 0.5 ]
[ true, true, true, true, true, true, true, true, true, true, true, false, true, true, true, false ]
[ 247, 434, 474, 448, 485, 472, 571, 520, 352, 424, 525, 634, 340, 537, 607, 699 ]
[[[6,9,5,4,2,8]],[[6,9,5,4,2,8]],[[6,9,5,4,2,8]],[[6,9,5,4,2,8]],[[6,9,5,4,2,8]],[[6,9,5,4,2,8]],[[6(...TRUNCATED)
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["The transformation rule involves identifying the object(s) made of non-zero colors in the input, m(...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 0, 0, 0, 0, 0, 0], [6, 6, (...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0](...TRUNCATED)
barc_heavy
"```\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0\n0 1 1 0 0 0 0 0 0\n0 1 1 0 0 0 0 0 0\(...TRUNCATED)
1,132
6.625
0.91821
0
529.3125
[ 4, 8, 8, 4, 4, 4, 8, 8, 8, 6, 4, 8, 8, 8, 8, 8 ]
[0.9506172839506173,0.9012345679012346,0.9012345679012346,0.9506172839506173,0.9506172839506173,0.95(...TRUNCATED)
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
[ 513, 400, 542, 512, 546, 488, 400, 609, 375, 832, 646, 681, 383, 631, 437, 474 ]
[[[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,0(...TRUNCATED)
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["The transformation rule observed across the examples is based on identifying connected components (...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 8, 4, 0, 0, 0, 0, 0, 0], [0, 4, 8, 4, 0, 0, 0,(...TRUNCATED)
"[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 2, 2, 0, 0, 0, 0, 0], [0, 3, 3, 2, 0, 0, 0, 0, 0](...TRUNCATED)
arc 1
"```\n0 0 0 0 0 0 0 0 0\n0 2 3 3 0 0 0 0 0\n0 2 2 3 0 0 0 0 0\n0 2 3 3 0 0 0 0 0\n0 0 0 0 0 1 1 1 0\(...TRUNCATED)
1,702
4.75
0.934028
0.875
626.875
[ 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 4, 0, 0 ]
[ 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0.9444444444444444, 1, 1 ]
[ true, true, true, true, true, true, false, true, true, true, true, true, true, false, true, true ]
[ 430, 477, 501, 505, 571, 448, 1164, 444, 486, 441, 539, 439, 499, 2100, 451, 535 ]
[[[0,0,0,0,0,0,0,0,0],[0,2,3,3,0,0,0,0,0],[0,2,2,3,0,0,0,0,0],[0,2,3,3,0,0,0,0,0],[0,0,0,0,0,1,1,1,0(...TRUNCATED)
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["The transformation rule observed across the examples involves reducing the width of the grid while(...TRUNCATED)
"[{\"input\": [[4, 4, 4, 4, 1, 0, 0, 0, 0], [0, 4, 0, 4, 1, 4, 0, 0, 0], [4, 0, 0, 0, 1, 0, 4, 0, 0](...TRUNCATED)
"[{\"input\": [[0, 0, 4, 0, 1, 0, 0, 4, 0], [4, 0, 4, 4, 1, 4, 4, 0, 4], [0, 0, 0, 4, 1, 4, 4, 0, 4](...TRUNCATED)
arc 1
``` 0 0 8 0 8 8 8 8 8 8 0 8 8 8 8 0 8 8 8 8 8 8 0 8 ```
1,188
0.25
0.989583
0.875
898.625
[ 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
[ 1, 1, 1, 0.875, 0.9583333333333334, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
[ true, true, true, false, false, true, true, true, true, true, true, true, true, true, true, true ]
[ 958, 873, 578, 2754, 692, 590, 805, 832, 574, 820, 913, 922, 658, 804, 732, 873 ]
[[[0,0,8,0],[8,8,8,8],[8,8,0,8],[8,8,8,0],[8,8,8,8],[8,8,0,8]],[[0,0,8,0],[8,8,8,8],[8,8,0,8],[8,8,8(...TRUNCATED)
"You will be given some number of paired example inputs and outputs grids. The outputs were produced(...TRUNCATED)
["This problem involves identifying structural components (non-background elements) in the input gri(...TRUNCATED)
"[{\"input\": [[6, 6, 6, 6, 6, 6, 6, 6], [9, 9, 9, 9, 6, 6, 6, 6], [9, 9, 9, 9, 6, 9, 9, 9], [0, 0, (...TRUNCATED)
"[{\"input\": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0], [6, 6(...TRUNCATED)
arc 2
"```\n6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 0 0 0 0\n6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6(...TRUNCATED)
3,606
541.375
0.199149
0
5,200
[ 676, 284, 676, 376, 676, 676, 328, 252, 676, 676, 282, 676, 676, 676, 676, 380 ]
[0.0,0.5798816568047337,0.0,0.4437869822485207,0.0,0.0,0.514792899408284,0.6272189349112426,0.0,0.0,(...TRUNCATED)
[ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false ]
[ 4050, 2435, 6804, 6647, 7639, 7876, 7680, 4378, 2261, 1997, 4244, 7906, 2794, 7882, 5657, 2950 ]
[null,[[6,6,6,6,6,6,6,6,6,6,6,0,0,0,0,0,6,6,6,6,6,6,0,0,0,0],[6,6,6,6,6,6,6,6,6,6,6,0,7,7,7,0,6,6,6,(...TRUNCATED)
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