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Results

All results obtained using SolverCUDA from one of the following systems:

  1. NVIDIA GeForce RTX 4090, 13th Gen Intel(R) Core(TM) i9-13900K, CUDA Toolkit 12.2 on Ubuntu 22.04.2 LTS, 5.15.90.1-microsoft-standard-WSL2

I only show results for games where I've determined the best starting guess which yields the lowest maximum turns, then the lowest average turns. This takes a long time for larger games, thus the tables are only partially filled.

All runs have all gameplay optimizations enabled, like small fully discriminating sets, case equivalence, etc. See Mastermind on the GPU for details. Note: for the CUDA impl, the case equivalence opt applies when $c^p > 400000$.

Times reported are from the first system unless otherwise marked. Raw data is in the .json files in subdirectories here.

Average turns over all games

Knuth

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 2.0000 2.3333 2.8125 3.3600 3.6667 4.1224 4.4531 4.8642 5.2000 5.5868 5.9236 6.2959 6.6326 6.9956
3p 2.2500 2.7407 3.2656 3.6400 4.0463 4.4140 4.7871 5.1824 5.5050 5.8107 6.1291 6.4329 6.7085 7.0006
4p 2.7500 3.0741 3.5898 4.0336 4.4761 4.8367 5.1831 5.5053 5.8103 6.1408 6.4177 6.7223 7.0014 7.3959
5p 3.0312 3.4074 3.9824 4.4374 4.8772 5.2321 5.6084 5.9507 6.2656 6.5547 6.8587 7.1615 7.4602 7.7118
6p 3.5156 3.7435 4.3787 4.8696 5.3186 5.7151 6.0867 6.4289 6.7372 7.0563 7.3499 7.6248 7.9085 8.1726
7p 4.0000 4.1367 4.7997 5.3401 5.8044 6.2222 6.6100 6.9710 7.2908 7.6011 7.8941 8.1754
8p 4.3984 4.5138 5.2406 5.8407 6.3456 6.7802 7.1810 7.5542

Most Parts

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 2.0000 2.3333 2.8125 3.2400 3.6667 4.0612 4.4531 4.8272 5.2000 5.5620 5.9236 6.2781 6.6326 6.9822
3p 2.2500 2.7037 3.2188 3.6240 3.9769 4.3498 4.7012 5.0316 5.3770 5.7077 6.0347 6.3673 6.6928 7.0169
4p 2.7500 3.0370 3.5547 3.9568 4.3735 4.7430 5.0874 5.3999 5.7320 6.3312 6.3777 6.7027 7.0294 7.3563
5p 3.0312 3.3580 3.8799 4.3514 4.8322 5.1686 5.5491 5.9035 6.2502 6.5941 6.9381 7.2716 7.6014 7.9318
6p 3.5000 3.6653 4.2676 4.7807 5.2336 5.6554 6.0275 6.3920 6.7433 7.0934 7.4425 7.8573 8.1291 8.5658
7p 3.9531 4.0210 4.6763 5.2409 5.7253 6.3962 6.5526 6.9279 7.2910 7.6484 8.0217 8.3514
8p 4.3867 4.3976 5.1320 5.7528 6.2755 6.7353 7.1544 7.5448

Expected Size

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 2.0000 2.3333 2.8125 3.2400 3.6667 4.0408 4.4375 4.7901 5.1700 5.5124 5.8819 6.2189 6.5816 6.9156
3p 2.2500 2.7037 3.2344 3.6320 3.9769 4.3411 4.6934 5.0055 5.3920 5.6995 5.9832 6.3077 6.6017 6.8738
4p 2.7500 3.0370 3.5781 3.9760 4.4475 4.7530 5.0598 5.3396 5.6940 5.9356 6.2244 6.4892 6.7640 7.0225
5p 3.0312 3.3580 3.9062 4.3693 4.7759 5.1521 5.4997 5.8168 6.1152 6.5396 6.8616 7.2504 7.7405 8.1590
6p 3.5000 3.6708 4.2920 4.8058 5.2117 5.6040 5.9610 6.4650 6.8712 7.3345 7.8254 8.2320 8.6830 9.1092
7p 3.9531 4.0338 4.6968 5.2294 5.6915 6.1978 6.6694 7.1081 7.5439 8.0010
8p 4.3789 4.4097 5.1351 5.7233 6.3377 6.8702 7.2923

Entropy

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 2.0000 2.3333 2.8125 3.2400 3.6667 4.0408 4.4375 4.7901 5.1700 5.5124 5.8819 6.2189 6.5867 6.9200
3p 2.2500 2.7037 3.2344 3.6240 3.9861 4.3353 4.6777 5.0014 5.3090 5.6439 5.9340 6.2813 6.5758 6.8495
4p 2.7500 3.0370 3.5586 3.9616 4.3850 4.7372 5.0525 5.3254 5.6225 5.9115 6.1819 6.4456 6.7133 6.9750
5p 3.0312 3.3580 3.8848 4.3514 4.8268 5.1414 5.4856 5.8073 6.1075 6.3823 6.6487 6.9054 7.1525 7.4905
6p 3.5312 3.6584 4.2588 4.7818 5.1972 5.5954 5.9535 6.2847 6.5971 6.8904 7.1669 7.4254 7.6785 7.9200
7p 3.9375 4.0270 4.6738 5.2128 5.6765 6.0880 6.4661 6.8075 7.1291 7.4309
8p 4.3711 4.3856 5.1111 5.6938 6.1951 6.6301 7.1621

Max turns over all games

Knuth

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 3 3 4 5 5 6 6 7 7 8 8 9 9 10
3p 3 4 4 5 5 6 6 7 7 7 8 8 8 9
4p 4 4 4 5 5 6 6 7 7 8 8 9 9 9
5p 4 4 5 6 6 7 7 8 8 9 9 9 10 10
6p 5 5 6 6 7 8 8 9 9 9 10 10 10 11
7p 6 5 6 7 8 8 9 9 10 10 11 11
8p 6 6 7 8 9 9 10 10

Most Parts

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 3 3 4 4 5 5 6 6 7 7 8 8 9 9
3p 3 4 4 5 5 6 6 7 7 8 8 9 9 10
4p 4 4 5 5 6 6 7 7 8 8 9 9 10 10
5p 4 4 5 6 6 7 8 8 9 9 10 10 11 11
6p 5 5 6 7 8 8 9 9 10 10 11 11 12 12
7p 6 6 7 8 9 9 10 11 11 12 12 13
8p 6 6 7 9 10 11 12 12

Expected Size

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 3 3 4 4 5 5 6 6 7 7 8 8 9 9
3p 3 4 4 5 5 6 6 7 7 7 8 8 8 9
4p 4 4 4 5 5 6 7 7 7 8 8 9 9 9
5p 4 4 5 6 6 7 7 8 8 9 9 10 10 11
6p 5 5 6 6 7 8 8 9 10 11 11 12 13 14
7p 6 5 6 7 8 9 9 10 11 12
8p 6 6 7 8 9 10 10

Entropy

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 3 3 4 4 5 5 6 6 7 7 8 8 9 9
3p 3 4 4 5 5 6 6 7 7 7 8 8 8 9
4p 4 4 4 5 6 6 7 7 8 8 8 9 9 9
5p 4 4 5 6 6 7 7 8 8 9 9 10 10 10
6p 5 5 6 6 7 8 8 9 9 10 10 10 11 11
7p 6 5 6 7 8 9 9 10 10 11
8p 6 6 7 8 9 10 10

Run time

All times in seconds.

Knuth

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 0.004 0.002 0.003 0.003 0.004 0.003 0.004 0.004 0.005 0.004 0.005 0.004 0.006 0.005
3p 0.004 0.003 0.003 0.004 0.003 0.004 0.003 0.005 0.005 0.004 0.004 0.005 0.005 0.007
4p 0.005 0.003 0.003 0.003 0.003 0.004 0.005 0.007 0.012 0.010 0.018 0.027 0.038 0.080
5p 0.005 0.003 0.003 0.004 0.006 0.009 0.018 0.053 0.119 0.301 0.661 1.518 2.710 3.363
6p 0.004 0.003 0.005 0.009 0.029 0.106 0.407 1.385 3.967 7.536 23.574 67.654 134 201
7p 0.006 0.004 0.009 0.055 0.438 2.786 15.529 83.311 372 848 3,237 12,796
8p 0.006 0.007 0.048 0.993 14.887 141 959 8,850

Most Parts

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 0.002 0.003 0.002 0.002 0.003 0.003 0.004 0.004 0.005 0.004 0.005 0.004 0.004 0.005
3p 0.002 0.002 0.003 0.003 0.004 0.004 0.003 0.004 0.006 0.004 0.005 0.005 0.005 0.007
4p 0.003 0.002 0.003 0.002 0.004 0.004 0.005 0.006 0.010 0.040 0.019 0.026 0.040 0.058
5p 0.002 0.002 0.003 0.004 0.007 0.010 0.017 0.051 0.119 0.292 0.695 1.607 1.901 2.583
6p 0.003 0.003 0.004 0.009 0.026 0.106 0.402 1.367 2.934 6.278 13.636 21.218 56.701 80.141
7p 0.004 0.004 0.009 0.051 0.421 3.452 11.800 74.280 253 725 2,121 3,870
8p 0.004 0.005 0.045 0.929 12.379 127 844 6,586

Expected Size

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 0.002 0.002 0.002 0.002 0.003 0.003 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.004
3p 0.003 0.003 0.003 0.003 0.003 0.004 0.003 0.005 0.004 0.005 0.004 0.005 0.005 0.007
4p 0.003 0.003 0.002 0.003 0.040 0.003 0.006 0.006 0.014 0.010 0.019 0.024 0.035 0.050
5p 0.003 0.002 0.003 0.004 0.005 0.009 0.017 0.050 0.112 0.280 0.654 1.510 2.172 3.264
6p 0.003 0.003 0.005 0.013 0.027 0.101 0.404 1.203 3.710 7.052 12.923 26.205 52.187 104
7p 0.004 0.004 0.008 0.053 0.455 2.222 21.383 122 344 802
8p 0.004 0.005 0.047 0.950 12.887 184 1,538

Entropy

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 0.002 0.002 0.002 0.004 0.002 0.003 0.005 0.004 0.003 0.004 0.004 0.004 0.004 0.004
3p 0.002 0.003 0.002 0.003 0.003 0.004 0.003 0.005 0.004 0.005 0.005 0.006 0.005 0.007
4p 0.002 0.002 0.002 0.004 0.004 0.003 0.005 0.006 0.011 0.011 0.019 0.024 0.035 0.050
5p 0.002 0.004 0.003 0.004 0.031 0.009 0.018 0.049 0.116 0.271 0.631 1.426 2.691 3.815
6p 0.003 0.003 0.005 0.012 0.028 0.102 0.418 1.734 4.457 11.804 30.027 82.902 188 388
7p 0.004 0.004 0.009 0.054 0.464 2.980 14.536 99.703 414 1,597
8p 0.004 0.006 0.048 0.964 15.141 146 1,584

Initial guess

These were determined by running all unique initial guesses and selecting the one with the lowest average turns.

Knuth

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 12 12 12 12 12 12 12 12 12 12 12 12 12 12
3p 112 112 112 112 123 123 123 123 123 123 123 123 123 123
4p 1112 1123 1123 1123 1122 1234 1234 1234 1234 1234 1234 1234 1234 1123
5p 11122 11122 11223 11223 11223 11223 11223 11234 12345 12345 12345 12345 12345 11234
6p 111222 111223 112233 112233 111234 112234 112234 112234 112345 112234 112345 123456 123456 112345
7p 1111222 1112233 1112233 1112234 1122334 1122334 1122345 1112234 1122345 1122334 1122345 1123456
8p 11111222 11122233 11122334 11122334 11122334 11223344 11223344 11223345

Most Parts

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 12 12 12 12 12 12 12 12 12 12 12 12 12 12
3p 112 112 112 123 123 123 123 123 123 123 123 123 123 123
4p 1112 1123 1123 1123 1123 1123 1234 1234 1234 1122 1234 1234 1234 1234
5p 11122 11123 11223 11223 11122 11223 11223 11234 11234 11234 11234 12345 12345 12345
6p 111122 111223 111223 111223 112233 112234 112233 112234 112234 112234 112234 112233 112345 111234
7p 1111222 1111223 1112223 1112233 1112233 1234567 1122334 1122334 1122334 1122334 1122345 1122334
8p 11112222 11112223 11122233 11122233 11122233 11122334 11122334 11122334

Expected Size

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 12 12 12 12 12 12 12 12 12 12 12 12 12 12
3p 112 112 112 112 123 123 123 123 123 123 123 123 123 123
4p 1112 1123 1123 1123 1122 1234 1234 1234 1123 1234 1234 1234 1234 1234
5p 11122 11123 11223 11223 11223 11223 11223 11234 11234 11223 11234 12345 11234 11234
6p 111122 111223 111234 111234 112233 112234 112234 112233 123456 123456 112345 112345 112345 112345
7p 1111222 1112223 1112233 1112233 1112233 1112233 1234567 1234567 1234567 1234567
8p 11111222 11122233 11122233 11122334 11112223 11234567 12345678

Entropy

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 12 12 12 12 12 12 12 12 12 12 12 12 12 12
3p 112 112 112 123 123 123 123 123 123 123 123 123 123 123
4p 1112 1123 1123 1123 1123 1123 1234 1234 1234 1234 1234 1234 1234 1234
5p 11122 11123 11223 11223 11122 11223 11223 11234 11234 11234 11234 12345 12345 11223
6p 111122 111223 111223 112234 111223 112234 112233 112234 112234 112234 112234 112345 112345 112345
7p 1111222 1112223 1112233 1112233 1112233 1122334 1122334 1122334 1122334 1122345
8p 11112222 11122233 11122233 11122334 11122334 11122334 12345678

Codeword scores performed

Knuth

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 8 37 237 959 2,302 5,448 10,451 19,517 32,802 53,782 82,739 124,715 180,142 255,924
3p 27 349 4,655 20,308 82,076 246,048 666,360 1,552,939 3,239,900 6,293,479 11,574,141 20,124,334 33,365,298 54,072,587
4p 295 5,883 73,055 684,812 3,454,547 14,504,604 47,191,496 136,110,862 350,326,688 822,324,322 1,766,777,678 3,613,004,214 6,946,645,908 13,054,792,086
5p 1,146 63,357 1,742,819 19,962,957 151,389,136 806,379,304 3,455,514,359 12,492,630,435 38,804,382,440 108,709,981,374 279,019,798,351 664,458,801,621 221,997,737,749 192,694,591,994
6p 6,871 773,451 33,492,304 603,953,600 6,350,988,508 45,982,760,423 253,759,838,005 391,185,522,015 1,656,721,118,522 3,199,457,315,883 10,858,425,592,971 32,889,665,862,260 62,472,732,590,695 83,261,167,884,700
7p 33,385 8,430,875 658,538,021 18,024,115,236 267,526,288,124 1,688,549,605,473 12,071,528,765,135 43,526,479,577,075 202,563,623,599,338 454,226,266,052,537 1,786,843,116,423,295 7,241,968,681,210,185
8p 153,818 93,497,904 12,270,461,992 526,976,844,351 9,068,132,002,615 97,720,579,295,094 701,717,829,399,382 4,682,574,122,447,169

Most Parts

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 8 37 237 840 2,302 5,233 10,451 19,174 32,802 53,279 82,739 124,020 180,142 255,005
3p 27 348 4,387 20,860 85,152 251,739 671,218 1,533,518 3,236,027 6,375,811 11,708,574 20,572,084 34,634,326 56,079,986
4p 295 5,880 77,528 652,972 3,463,134 14,270,384 47,208,015 135,472,446 350,464,893 878,817,869 1,797,140,727 3,680,119,986 7,174,306,215 13,312,144,408
5p 1,146 63,919 1,614,138 19,550,530 152,135,569 806,052,142 3,472,351,604 12,614,051,942 39,772,670,331 112,444,933,934 290,373,086,196 694,294,146,799 90,988,224,939 136,084,491,252
6p 7,119 720,784 33,027,100 595,258,454 6,341,359,719 46,072,975,414 255,246,785,068 383,523,838,927 1,046,858,939,830 2,459,853,019,348 5,087,144,152,500 6,734,551,527,982 19,841,112,296,443 23,280,249,903,990
7p 35,705 8,459,920 637,840,915 17,927,773,941 267,261,019,920 2,601,990,666,174 8,880,122,701,504 38,504,450,538,551 133,497,278,948,495 386,646,879,778,684 1,150,080,343,861,908 2,049,146,692,910,936
8p 162,189 93,044,769 12,180,822,787 527,293,108,359 7,485,302,242,714 92,083,690,331,092 643,575,570,820,001 3,464,187,208,779,301

Expected Size

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 8 37 237 756 2,259 4,862 10,269 18,154 32,228 51,032 81,340 119,704 177,257 247,466
3p 27 348 4,379 20,307 83,362 242,810 645,654 1,488,796 3,147,410 6,120,529 11,164,205 19,602,641 32,673,475 52,519,289
4p 295 5,880 71,469 674,138 3,414,542 13,943,407 45,652,480 129,723,306 339,204,689 782,091,005 1,689,882,163 3,435,613,183 6,639,130,529 12,168,202,360
5p 1,146 62,416 1,705,150 19,655,689 145,002,496 788,677,783 3,358,602,869 12,111,253,903 37,711,653,297 108,629,719,737 279,857,499,313 678,186,317,197 83,320,978,338 127,159,880,291
6p 6,315 706,069 32,432,560 592,871,529 6,188,149,187 44,610,788,824 246,812,861,651 275,708,427,535 1,504,549,849,624 2,863,387,679,682 4,262,149,789,918 7,865,731,904,423 13,464,528,036,793 23,321,531,102,914
7p 31,201 8,279,821 629,713,290 17,524,870,209 260,398,373,052 1,092,172,939,382 17,016,283,283,955 66,068,747,261,859 184,234,347,122,086 411,275,065,012,046
8p 156,400 88,589,231 11,891,779,695 511,534,385,555 6,886,477,705,836 138,534,093,924,209 1,240,207,360,811,578

Entropy

2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c 13c 14c 15c
2p 8 37 237 756 2,259 4,862 10,269 18,154 32,228 51,032 81,340 119,704 177,258 247,467
3p 27 348 4,379 19,696 85,102 240,659 648,610 1,490,245 3,066,171 6,098,395 11,050,237 19,481,846 32,610,998 52,326,875
4p 295 5,880 70,979 661,683 3,416,360 13,902,154 45,715,242 130,339,726 332,329,994 779,981,695 1,675,611,376 3,405,477,137 6,569,120,811 12,084,250,313
5p 1,146 63,181 1,601,576 19,527,248 149,702,727 787,883,746 3,359,885,206 12,087,333,783 37,778,545,052 105,292,045,887 267,744,752,466 632,934,443,503 317,908,538,869 346,134,520,308
6p 6,317 703,901 33,015,522 588,525,525 6,190,771,615 44,686,332,233 247,164,602,609 543,555,521,863 1,864,615,331,489 5,499,350,695,255 14,318,938,189,045 41,345,836,241,048 94,618,989,667,561 192,025,742,386,105
7p 30,941 8,256,099 625,605,978 17,490,706,992 259,734,446,561 1,683,004,716,928 10,009,426,166,809 50,340,716,513,854 217,263,812,165,510 861,938,290,687,204
8p 150,395 88,589,586 11,837,060,563 508,673,859,696 8,962,484,316,997 98,143,129,935,191 1,227,502,324,546,207

Grouped by Game

The same metrics grouped by game, to easily compare algorithms.

2p2c

Avg Max Time (s) Initial guess Scores
Knuth 2.0000 3 0.004 12 8
Most Parts 2.0000 3 0.002 12 8
Expected Size 2.0000 3 0.002 12 8
Entropy 2.0000 3 0.002 12 8

2p3c

Avg Max Time (s) Initial guess Scores
Knuth 2.3333 3 0.002 12 37
Most Parts 2.3333 3 0.003 12 37
Expected Size 2.3333 3 0.002 12 37
Entropy 2.3333 3 0.002 12 37

2p4c

Avg Max Time (s) Initial guess Scores
Knuth 2.8125 4 0.003 12 237
Most Parts 2.8125 4 0.002 12 237
Expected Size 2.8125 4 0.002 12 237
Entropy 2.8125 4 0.002 12 237

2p5c

Avg Max Time (s) Initial guess Scores
Knuth 3.3600 5 0.003 12 959
Most Parts 3.2400 4 0.002 12 840
Expected Size 3.2400 4 0.002 12 756
Entropy 3.2400 4 0.004 12 756

2p6c

Avg Max Time (s) Initial guess Scores
Knuth 3.6667 5 0.004 12 2,302
Most Parts 3.6667 5 0.003 12 2,302
Expected Size 3.6667 5 0.003 12 2,259
Entropy 3.6667 5 0.002 12 2,259

2p7c

Avg Max Time (s) Initial guess Scores
Knuth 4.1224 6 0.003 12 5,448
Most Parts 4.0612 5 0.003 12 5,233
Expected Size 4.0408 5 0.003 12 4,862
Entropy 4.0408 5 0.003 12 4,862

2p8c

Avg Max Time (s) Initial guess Scores
Knuth 4.4531 6 0.004 12 10,451
Most Parts 4.4531 6 0.004 12 10,451
Expected Size 4.4375 6 0.004 12 10,269
Entropy 4.4375 6 0.005 12 10,269

2p9c

Avg Max Time (s) Initial guess Scores
Knuth 4.8642 7 0.004 12 19,517
Most Parts 4.8272 6 0.004 12 19,174
Expected Size 4.7901 6 0.004 12 18,154
Entropy 4.7901 6 0.004 12 18,154

2p10c

Avg Max Time (s) Initial guess Scores
Knuth 5.2000 7 0.005 12 32,802
Most Parts 5.2000 7 0.005 12 32,802
Expected Size 5.1700 7 0.004 12 32,228
Entropy 5.1700 7 0.003 12 32,228

2p11c

Avg Max Time (s) Initial guess Scores
Knuth 5.5868 8 0.004 12 53,782
Most Parts 5.5620 7 0.004 12 53,279
Expected Size 5.5124 7 0.004 12 51,032
Entropy 5.5124 7 0.004 12 51,032

2p12c

Avg Max Time (s) Initial guess Scores
Knuth 5.9236 8 0.005 12 82,739
Most Parts 5.9236 8 0.005 12 82,739
Expected Size 5.8819 8 0.005 12 81,340
Entropy 5.8819 8 0.004 12 81,340

2p13c

Avg Max Time (s) Initial guess Scores
Knuth 6.2959 9 0.004 12 124,715
Most Parts 6.2781 8 0.004 12 124,020
Expected Size 6.2189 8 0.004 12 119,704
Entropy 6.2189 8 0.004 12 119,704

2p14c

Avg Max Time (s) Initial guess Scores
Knuth 6.6326 9 0.006 12 180,142
Most Parts 6.6326 9 0.004 12 180,142
Expected Size 6.5816 9 0.004 12 177,257
Entropy 6.5867 9 0.004 12 177,258

2p15c

Avg Max Time (s) Initial guess Scores
Knuth 6.9956 10 0.005 12 255,924
Most Parts 6.9822 9 0.005 12 255,005
Expected Size 6.9156 9 0.004 12 247,466
Entropy 6.9200 9 0.004 12 247,467

3p2c

Avg Max Time (s) Initial guess Scores
Knuth 2.2500 3 0.004 112 27
Most Parts 2.2500 3 0.002 112 27
Expected Size 2.2500 3 0.003 112 27
Entropy 2.2500 3 0.002 112 27

3p3c

Avg Max Time (s) Initial guess Scores
Knuth 2.7407 4 0.003 112 349
Most Parts 2.7037 4 0.002 112 348
Expected Size 2.7037 4 0.003 112 348
Entropy 2.7037 4 0.003 112 348

3p4c

Avg Max Time (s) Initial guess Scores
Knuth 3.2656 4 0.003 112 4,655
Most Parts 3.2188 4 0.003 112 4,387
Expected Size 3.2344 4 0.003 112 4,379
Entropy 3.2344 4 0.002 112 4,379

3p5c

Avg Max Time (s) Initial guess Scores
Knuth 3.6400 5 0.004 112 20,308
Most Parts 3.6240 5 0.003 123 20,860
Expected Size 3.6320 5 0.003 112 20,307
Entropy 3.6240 5 0.003 123 19,696

3p6c

Avg Max Time (s) Initial guess Scores
Knuth 4.0463 5 0.003 123 82,076
Most Parts 3.9769 5 0.004 123 85,152
Expected Size 3.9769 5 0.003 123 83,362
Entropy 3.9861 5 0.003 123 85,102

3p7c

Avg Max Time (s) Initial guess Scores
Knuth 4.4140 6 0.004 123 246,048
Most Parts 4.3498 6 0.004 123 251,739
Expected Size 4.3411 6 0.004 123 242,810
Entropy 4.3353 6 0.004 123 240,659

3p8c

Avg Max Time (s) Initial guess Scores
Knuth 4.7871 6 0.003 123 666,360
Most Parts 4.7012 6 0.003 123 671,218
Expected Size 4.6934 6 0.003 123 645,654
Entropy 4.6777 6 0.003 123 648,610

3p9c

Avg Max Time (s) Initial guess Scores
Knuth 5.1824 7 0.005 123 1,552,939
Most Parts 5.0316 7 0.004 123 1,533,518
Expected Size 5.0055 7 0.005 123 1,488,796
Entropy 5.0014 7 0.005 123 1,490,245

3p10c

Avg Max Time (s) Initial guess Scores
Knuth 5.5050 7 0.005 123 3,239,900
Most Parts 5.3770 7 0.006 123 3,236,027
Expected Size 5.3920 7 0.004 123 3,147,410
Entropy 5.3090 7 0.004 123 3,066,171

3p11c

Avg Max Time (s) Initial guess Scores
Knuth 5.8107 7 0.004 123 6,293,479
Most Parts 5.7077 8 0.004 123 6,375,811
Expected Size 5.6995 7 0.005 123 6,120,529
Entropy 5.6439 7 0.005 123 6,098,395

3p12c

Avg Max Time (s) Initial guess Scores
Knuth 6.1291 8 0.004 123 11,574,141
Most Parts 6.0347 8 0.005 123 11,708,574
Expected Size 5.9832 8 0.004 123 11,164,205
Entropy 5.9340 8 0.005 123 11,050,237

3p13c

Avg Max Time (s) Initial guess Scores
Knuth 6.4329 8 0.005 123 20,124,334
Most Parts 6.3673 9 0.005 123 20,572,084
Expected Size 6.3077 8 0.005 123 19,602,641
Entropy 6.2813 8 0.006 123 19,481,846

3p14c

Avg Max Time (s) Initial guess Scores
Knuth 6.7085 8 0.005 123 33,365,298
Most Parts 6.6928 9 0.005 123 34,634,326
Expected Size 6.6017 8 0.005 123 32,673,475
Entropy 6.5758 8 0.005 123 32,610,998

3p15c

Avg Max Time (s) Initial guess Scores
Knuth 7.0006 9 0.007 123 54,072,587
Most Parts 7.0169 10 0.007 123 56,079,986
Expected Size 6.8738 9 0.007 123 52,519,289
Entropy 6.8495 9 0.007 123 52,326,875

4p2c

Avg Max Time (s) Initial guess Scores
Knuth 2.7500 4 0.005 1112 295
Most Parts 2.7500 4 0.003 1112 295
Expected Size 2.7500 4 0.003 1112 295
Entropy 2.7500 4 0.002 1112 295

4p3c

Avg Max Time (s) Initial guess Scores
Knuth 3.0741 4 0.003 1123 5,883
Most Parts 3.0370 4 0.002 1123 5,880
Expected Size 3.0370 4 0.003 1123 5,880
Entropy 3.0370 4 0.002 1123 5,880

4p4c

Avg Max Time (s) Initial guess Scores
Knuth 3.5898 4 0.003 1123 73,055
Most Parts 3.5547 5 0.003 1123 77,528
Expected Size 3.5781 4 0.002 1123 71,469
Entropy 3.5586 4 0.002 1123 70,979

4p5c

Avg Max Time (s) Initial guess Scores
Knuth 4.0336 5 0.003 1123 684,812
Most Parts 3.9568 5 0.002 1123 652,972
Expected Size 3.9760 5 0.003 1123 674,138
Entropy 3.9616 5 0.004 1123 661,683

4p6c

Avg Max Time (s) Initial guess Scores
Knuth 4.4761 5 0.003 1122 3,454,547
Most Parts 4.3735 6 0.004 1123 3,463,134
Expected Size 4.4475 5 0.040 1122 3,414,542
Entropy 4.3850 6 0.004 1123 3,416,360

4p7c

Avg Max Time (s) Initial guess Scores
Knuth 4.8367 6 0.004 1234 14,504,604
Most Parts 4.7430 6 0.004 1123 14,270,384
Expected Size 4.7530 6 0.003 1234 13,943,407
Entropy 4.7372 6 0.003 1123 13,902,154

4p8c

Avg Max Time (s) Initial guess Scores
Knuth 5.1831 6 0.005 1234 47,191,496
Most Parts 5.0874 7 0.005 1234 47,208,015
Expected Size 5.0598 7 0.006 1234 45,652,480
Entropy 5.0525 7 0.005 1234 45,715,242

4p9c

Avg Max Time (s) Initial guess Scores
Knuth 5.5053 7 0.007 1234 136,110,862
Most Parts 5.3999 7 0.006 1234 135,472,446
Expected Size 5.3396 7 0.006 1234 129,723,306
Entropy 5.3254 7 0.006 1234 130,339,726

4p10c

Avg Max Time (s) Initial guess Scores
Knuth 5.8103 7 0.012 1234 350,326,688
Most Parts 5.7320 8 0.010 1234 350,464,893
Expected Size 5.6940 7 0.014 1123 339,204,689
Entropy 5.6225 8 0.011 1234 332,329,994

4p11c

Avg Max Time (s) Initial guess Scores
Knuth 6.1408 8 0.010 1234 822,324,322
Most Parts 6.3312 8 0.040 1122 878,817,869
Expected Size 5.9356 8 0.010 1234 782,091,005
Entropy 5.9115 8 0.011 1234 779,981,695

4p12c

Avg Max Time (s) Initial guess Scores
Knuth 6.4177 8 0.018 1234 1,766,777,678
Most Parts 6.3777 9 0.019 1234 1,797,140,727
Expected Size 6.2244 8 0.019 1234 1,689,882,163
Entropy 6.1819 8 0.019 1234 1,675,611,376

4p13c

Avg Max Time (s) Initial guess Scores
Knuth 6.7223 9 0.027 1234 3,613,004,214
Most Parts 6.7027 9 0.026 1234 3,680,119,986
Expected Size 6.4892 9 0.024 1234 3,435,613,183
Entropy 6.4456 9 0.024 1234 3,405,477,137

4p14c

Avg Max Time (s) Initial guess Scores
Knuth 7.0014 9 0.038 1234 6,946,645,908
Most Parts 7.0294 10 0.040 1234 7,174,306,215
Expected Size 6.7640 9 0.035 1234 6,639,130,529
Entropy 6.7133 9 0.035 1234 6,569,120,811

4p15c

Avg Max Time (s) Initial guess Scores
Knuth 7.3959 9 0.080 1123 13,054,792,086
Most Parts 7.3563 10 0.058 1234 13,312,144,408
Expected Size 7.0225 9 0.050 1234 12,168,202,360
Entropy 6.9750 9 0.050 1234 12,084,250,313

5p2c

Avg Max Time (s) Initial guess Scores
Knuth 3.0312 4 0.005 11122 1,146
Most Parts 3.0312 4 0.002 11122 1,146
Expected Size 3.0312 4 0.003 11122 1,146
Entropy 3.0312 4 0.002 11122 1,146

5p3c

Avg Max Time (s) Initial guess Scores
Knuth 3.4074 4 0.003 11122 63,357
Most Parts 3.3580 4 0.002 11123 63,919
Expected Size 3.3580 4 0.002 11123 62,416
Entropy 3.3580 4 0.004 11123 63,181

5p4c

Avg Max Time (s) Initial guess Scores
Knuth 3.9824 5 0.003 11223 1,742,819
Most Parts 3.8799 5 0.003 11223 1,614,138
Expected Size 3.9062 5 0.003 11223 1,705,150
Entropy 3.8848 5 0.003 11223 1,601,576

5p5c

Avg Max Time (s) Initial guess Scores
Knuth 4.4374 6 0.004 11223 19,962,957
Most Parts 4.3514 6 0.004 11223 19,550,530
Expected Size 4.3693 6 0.004 11223 19,655,689
Entropy 4.3514 6 0.004 11223 19,527,248

5p6c

Avg Max Time (s) Initial guess Scores
Knuth 4.8772 6 0.006 11223 151,389,136
Most Parts 4.8322 6 0.007 11122 152,135,569
Expected Size 4.7759 6 0.005 11223 145,002,496
Entropy 4.8268 6 0.031 11122 149,702,727

5p7c

Avg Max Time (s) Initial guess Scores
Knuth 5.2321 7 0.009 11223 806,379,304
Most Parts 5.1686 7 0.010 11223 806,052,142
Expected Size 5.1521 7 0.009 11223 788,677,783
Entropy 5.1414 7 0.009 11223 787,883,746

5p8c

Avg Max Time (s) Initial guess Scores
Knuth 5.6084 7 0.018 11223 3,455,514,359
Most Parts 5.5491 8 0.017 11223 3,472,351,604
Expected Size 5.4997 7 0.017 11223 3,358,602,869
Entropy 5.4856 7 0.018 11223 3,359,885,206

5p9c

Avg Max Time (s) Initial guess Scores
Knuth 5.9507 8 0.053 11234 12,492,630,435
Most Parts 5.9035 8 0.051 11234 12,614,051,942
Expected Size 5.8168 8 0.050 11234 12,111,253,903
Entropy 5.8073 8 0.049 11234 12,087,333,783

5p10c

Avg Max Time (s) Initial guess Scores
Knuth 6.2656 8 0.119 12345 38,804,382,440
Most Parts 6.2502 9 0.119 11234 39,772,670,331
Expected Size 6.1152 8 0.112 11234 37,711,653,297
Entropy 6.1075 8 0.116 11234 37,778,545,052

5p11c

Avg Max Time (s) Initial guess Scores
Knuth 6.5547 9 0.301 12345 108,709,981,374
Most Parts 6.5941 9 0.292 11234 112,444,933,934
Expected Size 6.5396 9 0.280 11223 108,629,719,737
Entropy 6.3823 9 0.271 11234 105,292,045,887

5p12c

Avg Max Time (s) Initial guess Scores
Knuth 6.8587 9 0.661 12345 279,019,798,351
Most Parts 6.9381 10 0.695 11234 290,373,086,196
Expected Size 6.8616 9 0.654 11234 279,857,499,313
Entropy 6.6487 9 0.631 11234 267,744,752,466

5p13c

Avg Max Time (s) Initial guess Scores
Knuth 7.1615 9 1.518 12345 664,458,801,621
Most Parts 7.2716 10 1.607 12345 694,294,146,799
Expected Size 7.2504 10 1.510 12345 678,186,317,197
Entropy 6.9054 10 1.426 12345 632,934,443,503

5p14c

Avg Max Time (s) Initial guess Scores
Knuth 7.4602 10 2.710 12345 221,997,737,749
Most Parts 7.6014 11 1.901 12345 90,988,224,939
Expected Size 7.7405 10 2.172 11234 83,320,978,338
Entropy 7.1525 10 2.691 12345 317,908,538,869

5p15c

Avg Max Time (s) Initial guess Scores
Knuth 7.7118 10 3.363 11234 192,694,591,994
Most Parts 7.9318 11 2.583 12345 136,084,491,252
Expected Size 8.1590 11 3.264 11234 127,159,880,291
Entropy 7.4905 10 3.815 11223 346,134,520,308

6p2c

Avg Max Time (s) Initial guess Scores
Knuth 3.5156 5 0.004 111222 6,871
Most Parts 3.5000 5 0.003 111122 7,119
Expected Size 3.5000 5 0.003 111122 6,315
Entropy 3.5312 5 0.003 111122 6,317

6p3c

Avg Max Time (s) Initial guess Scores
Knuth 3.7435 5 0.003 111223 773,451
Most Parts 3.6653 5 0.003 111223 720,784
Expected Size 3.6708 5 0.003 111223 706,069
Entropy 3.6584 5 0.003 111223 703,901

6p4c

Avg Max Time (s) Initial guess Scores
Knuth 4.3787 6 0.005 112233 33,492,304
Most Parts 4.2676 6 0.004 111223 33,027,100
Expected Size 4.2920 6 0.005 111234 32,432,560
Entropy 4.2588 6 0.005 111223 33,015,522

6p5c

Avg Max Time (s) Initial guess Scores
Knuth 4.8696 6 0.009 112233 603,953,600
Most Parts 4.7807 7 0.009 111223 595,258,454
Expected Size 4.8058 6 0.013 111234 592,871,529
Entropy 4.7818 6 0.012 112234 588,525,525

6p6c

Avg Max Time (s) Initial guess Scores
Knuth 5.3186 7 0.029 111234 6,350,988,508
Most Parts 5.2336 8 0.026 112233 6,341,359,719
Expected Size 5.2117 7 0.027 112233 6,188,149,187
Entropy 5.1972 7 0.028 111223 6,190,771,615

6p7c

Avg Max Time (s) Initial guess Scores
Knuth 5.7151 8 0.106 112234 45,982,760,423
Most Parts 5.6554 8 0.106 112234 46,072,975,414
Expected Size 5.6040 8 0.101 112234 44,610,788,824
Entropy 5.5954 8 0.102 112234 44,686,332,233

6p8c

Avg Max Time (s) Initial guess Scores
Knuth 6.0867 8 0.407 112234 253,759,838,005
Most Parts 6.0275 9 0.402 112233 255,246,785,068
Expected Size 5.9610 8 0.404 112234 246,812,861,651
Entropy 5.9535 8 0.418 112233 247,164,602,609

6p9c

Avg Max Time (s) Initial guess Scores
Knuth 6.4289 9 1.385 112234 391,185,522,015
Most Parts 6.3920 9 1.367 112234 383,523,838,927
Expected Size 6.4650 9 1.203 112233 275,708,427,535
Entropy 6.2847 9 1.734 112234 543,555,521,863

6p10c

Avg Max Time (s) Initial guess Scores
Knuth 6.7372 9 3.967 112345 1,656,721,118,522
Most Parts 6.7433 10 2.934 112234 1,046,858,939,830
Expected Size 6.8712 10 3.710 123456 1,504,549,849,624
Entropy 6.5971 9 4.457 112234 1,864,615,331,489

6p11c

Avg Max Time (s) Initial guess Scores
Knuth 7.0563 9 7.536 112234 3,199,457,315,883
Most Parts 7.0934 10 6.278 112234 2,459,853,019,348
Expected Size 7.3345 11 7.052 123456 2,863,387,679,682
Entropy 6.8904 10 11.804 112234 5,499,350,695,255

6p12c

Avg Max Time (s) Initial guess Scores
Knuth 7.3499 10 23.574 112345 10,858,425,592,971
Most Parts 7.4425 11 13.636 112234 5,087,144,152,500
Expected Size 7.8254 11 12.923 112345 4,262,149,789,918
Entropy 7.1669 10 30.027 112234 14,318,938,189,045

6p13c

Avg Max Time (s) Initial guess Scores
Knuth 7.6248 10 67.654 123456 32,889,665,862,260
Most Parts 7.8573 11 21.218 112233 6,734,551,527,982
Expected Size 8.2320 12 26.205 112345 7,865,731,904,423
Entropy 7.4254 10 82.902 112345 41,345,836,241,048

6p14c

Avg Max Time (s) Initial guess Scores
Knuth 7.9085 10 134.804 123456 62,472,732,590,695
Most Parts 8.1291 12 56.701 112345 19,841,112,296,443
Expected Size 8.6830 13 52.187 112345 13,464,528,036,793
Entropy 7.6785 11 188.688 112345 94,618,989,667,561

6p15c

Avg Max Time (s) Initial guess Scores
Knuth 8.1726 11 201.088 112345 83,261,167,884,700
Most Parts 8.5658 12 80.141 111234 23,280,249,903,990
Expected Size 9.1092 14 104.482 112345 23,321,531,102,914
Entropy 7.9200 11 388.264 112345 192,025,742,386,105

7p2c

Avg Max Time (s) Initial guess Scores
Knuth 4.0000 6 0.006 1111222 33,385
Most Parts 3.9531 6 0.004 1111222 35,705
Expected Size 3.9531 6 0.004 1111222 31,201
Entropy 3.9375 6 0.004 1111222 30,941

7p3c

Avg Max Time (s) Initial guess Scores
Knuth 4.1367 5 0.004 1112233 8,430,875
Most Parts 4.0210 6 0.004 1111223 8,459,920
Expected Size 4.0338 5 0.004 1112223 8,279,821
Entropy 4.0270 5 0.004 1112223 8,256,099

7p4c

Avg Max Time (s) Initial guess Scores
Knuth 4.7997 6 0.009 1112233 658,538,021
Most Parts 4.6763 7 0.009 1112223 637,840,915
Expected Size 4.6968 6 0.008 1112233 629,713,290
Entropy 4.6738 6 0.009 1112233 625,605,978

7p5c

Avg Max Time (s) Initial guess Scores
Knuth 5.3401 7 0.055 1112234 18,024,115,236
Most Parts 5.2409 8 0.051 1112233 17,927,773,941
Expected Size 5.2294 7 0.053 1112233 17,524,870,209
Entropy 5.2128 7 0.054 1112233 17,490,706,992

7p6c

Avg Max Time (s) Initial guess Scores
Knuth 5.8044 8 0.438 1122334 267,526,288,124
Most Parts 5.7253 9 0.421 1112233 267,261,019,920
Expected Size 5.6915 8 0.455 1112233 260,398,373,052
Entropy 5.6765 8 0.464 1112233 259,734,446,561

7p7c

Avg Max Time (s) Initial guess Scores
Knuth 6.2222 8 2.786 1122334 1,688,549,605,473
Most Parts 6.3962 9 3.452 1234567 2,601,990,666,174
Expected Size 6.1978 9 2.222 1112233 1,092,172,939,382
Entropy 6.0880 9 2.980 1122334 1,683,004,716,928

7p8c

Avg Max Time (s) Initial guess Scores
Knuth 6.6100 9 15.529 1122345 12,071,528,765,135
Most Parts 6.5526 10 11.800 1122334 8,880,122,701,504
Expected Size 6.6694 9 21.383 1234567 17,016,283,283,955
Entropy 6.4661 9 14.536 1122334 10,009,426,166,809

7p9c

Avg Max Time (s) Initial guess Scores
Knuth 6.9710 9 83.311 1112234 43,526,479,577,075
Most Parts 6.9279 11 74.280 1122334 38,504,450,538,551
Expected Size 7.1081 10 122.774 1234567 66,068,747,261,859
Entropy 6.8075 10 99.703 1122334 50,340,716,513,854

7p10c

Avg Max Time (s) Initial guess Scores
Knuth 7.2908 10 372.325 1122345 202,563,623,599,338
Most Parts 7.2910 11 253.766 1122334 133,497,278,948,495
Expected Size 7.5439 11 344.760 1234567 184,234,347,122,086
Entropy 7.1291 10 414.770 1122334 217,263,812,165,510

7p11c

Avg Max Time (s) Initial guess Scores
Knuth 7.6011 10 848.520 1122334 454,226,266,052,537
Most Parts 7.6484 12 725.662 1122334 386,646,879,778,684
Expected Size 8.0010 12 802.692 1234567 411,275,065,012,046
Entropy 7.4309 11 1,597.259 1122345 861,938,290,687,204

7p12c

Avg Max Time (s) Initial guess Scores
Knuth 7.8941 11 3,237.639 1122345 1,786,843,116,423,295
Most Parts 8.0217 12 2,121.739 1122345 1,150,080,343,861,908

7p13c

Avg Max Time (s) Initial guess Scores
Knuth 8.1754 11 12,796.380 1123456 7,241,968,681,210,185
Most Parts 8.3514 13 3,870.832 1122334 2,049,146,692,910,936

8p2c

Avg Max Time (s) Initial guess Scores
Knuth 4.3984 6 0.006 11111222 153,818
Most Parts 4.3867 6 0.004 11112222 162,189
Expected Size 4.3789 6 0.004 11111222 156,400
Entropy 4.3711 6 0.004 11112222 150,395

8p3c

Avg Max Time (s) Initial guess Scores
Knuth 4.5138 6 0.007 11122233 93,497,904
Most Parts 4.3976 6 0.005 11112223 93,044,769
Expected Size 4.4097 6 0.005 11122233 88,589,231
Entropy 4.3856 6 0.006 11122233 88,589,586

8p4c

Avg Max Time (s) Initial guess Scores
Knuth 5.2406 7 0.048 11122334 12,270,461,992
Most Parts 5.1320 7 0.045 11122233 12,180,822,787
Expected Size 5.1351 7 0.047 11122233 11,891,779,695
Entropy 5.1111 7 0.048 11122233 11,837,060,563

8p5c

Avg Max Time (s) Initial guess Scores
Knuth 5.8407 8 0.993 11122334 526,976,844,351
Most Parts 5.7528 9 0.929 11122233 527,293,108,359
Expected Size 5.7233 8 0.950 11122334 511,534,385,555
Entropy 5.6938 8 0.964 11122334 508,673,859,696

8p6c

Avg Max Time (s) Initial guess Scores
Knuth 6.3456 9 14.887 11122334 9,068,132,002,615
Most Parts 6.2755 10 12.379 11122233 7,485,302,242,714
Expected Size 6.3377 9 12.887 11112223 6,886,477,705,836
Entropy 6.1951 9 15.141 11122334 8,962,484,316,997

8p7c

Avg Max Time (s) Initial guess Scores
Knuth 6.7802 9 141.475 11223344 97,720,579,295,094
Most Parts 6.7353 11 127.750 11122334 92,083,690,331,092
Expected Size 6.8702 10 184.254 11234567 138,534,093,924,209
Entropy 6.6301 10 146.538 11122334 98,143,129,935,191

8p8c

Avg Max Time (s) Initial guess Scores
Knuth 7.1810 10 959.758 11223344 701,717,829,399,382
Most Parts 7.1544 12 844.263 11122334 643,575,570,820,001
Expected Size 7.2923 10 1,538.505 12345678 1,240,207,360,811,578
Entropy 7.1621 10 1,584.364 12345678 1,227,502,324,546,207

8p9c

Avg Max Time (s) Initial guess Scores
Knuth 7.5542 10 8,850.113 11223345 4,682,574,122,447,169
Most Parts 7.5448 12 6,586.134 11122334 3,464,187,208,779,301