http://www.ericharshbarger.org/wiki/ 2026-10-17T06:34:17+00:00 http://www.ericharshbarger.org/wiki/ http://www.ericharshbarger.org/wiki/lib/tpl/dokuwiki/images/favicon.ico text/html 2024-01-28T15:05:44+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=4d36_d20&rev=1706454344&do=diff This page contains all of the unique permutation-fair 4d36+d20 configurations of Go First Dice that have been discovered so far. Die-wise permutations and trivial substitutions (e.g. “abba” -> “baab”) are pruned for conciseness. Note that all solutions thus far have been found by constructing an text/html 2026-09-27T02:04:44+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=4d48_d20&rev=1790474684&do=diff This page demonstrates a permutation-fair d20 + 4d48 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. abccbaddddabccbaeeeeabccbaddddabccbaddbccabaabaccbddedcabbacddbaccabdedbaccabddcabbacdeeeeedbaccabddcabbacdedcabbacddbaccabdabccbaddddabccbaabccbaddddabccbaeeeeeabccbaddddabccbaeabccbaddddabccbaeddbccabaabaccbdde text/html 2024-01-28T18:11:42+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=4d48_d30&rev=1706465502&do=diff This page contains all of the unique permutation-fair 4d48+d30 configurations of Go First Dice that have been discovered so far. Die-wise permutations and trivial substitutions (e.g. “abba” -> “baab”) are pruned for conciseness. Note that all solutions thus far have been found by constructing an text/html 2024-01-28T15:05:01+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=4d60_d20&rev=1706454301&do=diff This page contains all of the unique permutation-fair 4d60+d20 configurations of Go First Dice that have been discovered so far. Die-wise permutations and trivial substitutions (e.g. “abba” -> “baab”) are pruned for conciseness. Note that all solutions thus far have been found by constructing an text/html 2024-09-12T18:40:26+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=5d60&rev=1726166426&do=diff This page contains the first discovered set of permutation-fair 5d60 configurations of Go First Dice. After developing an improved search algorithm, many millions more have been discovered since. Die-wise permutations and trivial substitutions (e.g. text/html 2026-10-15T14:27:40+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=6d120&rev=1792074460&do=diff This page demonstrates a permutation-fair 6d120 configuration of Go First Dice, discovered by Paul Meyer on Oct 15, 2026. efefeabcddcbadbaccabdfffdbaccabdeeffedbaccabdffcbaddabceeeeefecbaddabcfffabcddcbaeefefcbaddabcfffabcddcbaeeeeeefeeedbaccabdfffcbaddabceeeabcddcbaffcbaddabcfabcddcbafffffcbaddabceefeabcddcbafffffdbaccabdfeeecbaddabcabcddcbaeeeeeecbaddabcfffabcddcbaeefedbaccabdfffeffeeabcddcbaefeecbaddabceeefdbaccabdeefffefdbaccabdeeffeabcddcbafcbaddabcffffdbaccabdeeedbaccabdffdbaccabdeeedbacc… text/html 2024-09-20T13:29:32+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=7d10080&rev=1726838972&do=diff This page demonstrates a go first fair 7d10080 configuration, found by Paul Meyer on Sept 17, 2024. This configuration was constructed as follows: 1. Repeat a fair 5d60 config 6 times to get a fair 5d360. 2. Induce a d20 around the repetitions and multiply it 18 times to get a fair 6d360. text/html 2024-09-12T18:37:15+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d20_4d60&rev=1726166235&do=diff abcddcbaecbaddabcabcddcbaeedbaccabddbaccabdeecbaddabcabcddcbadbaccabddbaccabdecbaddabccbaddabcecbaddabcdbaccabdeeabcddcbaecbaddabceedbaccabdabcddcbacbaddabcabcddcbaeabcddcbadbaccabdeeabcddcbadbaccabdabcddcbaecbaddabcecbaddabcedbaccabdabcddcbaedbaccabdecbaddabc text/html 2026-09-27T02:09:51+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d20_4d72_d120&rev=1790474991&do=diff This page demonstrates a permutation-fair d20 + 4d72 + d120 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. feabcddcbaeeeeecbaddabcedbaccabdeeeeeedbaccabdecbaddabceeeeeabcddcbaefffffecbaddabceeeeedbaccabdeabcddcbaeeeeeeabcddcbaedbaccabdeeeeecbaddabcefedbaccabdeeeeeabcddcbaecbaddabceeeeeecbaddabceabcddcbaeeeeedbaccabdeffffffedbaccabdeeeeeabcddcbaecbaddabceeeeeecbaddabceabcddcbaeeeeedbaccabdefecbaddabceeeeedbaccabdeabcddcbaeeeeeeabcddcbaedbaccabdeeeeecbaddabcefffffeabcddcbae… text/html 2026-09-26T13:47:25+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d20_5d180&rev=1790430445&do=diff This page demonstrates a permutation-fair d20 + 5d180 configuration of Go First Dice, found by Paul Meyer on Sept 25, 2026. With an LCM of 180, this solution can be scaled to a homogeneous 6d180. fffdabccbadcabddbacbacddcabfffefffbacddcabcabddbacdabccbadffffeffdabccbadcabddbacbacddcabefffffdabccbadcabddbacbacddcabffffbacddcabcabddbacdabccbadfffffffffffffbacddcabcabddbacdabccbadffefbacddcabcabddbacdabccbadfffffebacddcabcabddbacdabccbadfffffdabccbadcabddbacbacddcabffeffebacddcabcabddbacdabccbadf… text/html 2024-09-12T18:33:34+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d20_d120_4d360&rev=1726166014&do=diff The following d20+d120+4d360 configuration was found by Paul Meyer after the original 6d360 record, though the LCM is not improved. It is constructed by inducing a d20 around 6 repetitions of Paul's d20+4d60 configuration. fabcddcbaecbaddabcabcddcbaeedbaccabddbaccabdeecbaddabcabcddcbadbaccabddbaccabdecbaddabccbaddabcecbaddabcdbaccabdeeabcddcbaecbaddabceedbaccabdabcddcbacbaddabcabcddcbaeabcddcbadbaccabdeeabcddcbadbaccabdabcddcbaecbaddabcecbaddabcedbaccabdabcddcbaedbaccabdecbaddabcfffffabcddcbaec… text/html 2026-09-26T00:50:39+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d80_d120_4d240&rev=1790383839&do=diff This page demonstrates a permutation-fair d80 + d120 + 4d240 configuration of Go First Dice, found by Paul Meyer on Sept 25, 2026. eeffabccbaddddabccbaddbccbaaaabccbddfffffddbccbaaaabccbddabccbaddddabccbaeeffeeeeabccbaddddabccbaddbccbaaaabccbddffefeeabccbaddddabccbaabccbaddddabccbaffffffffabccbaddddabccbaddbccbaaaabccbddeeabccbaddddabccbaabccbaddddabccbaeefffffefffeabccbaddddabccbaabccbaddddabccbaeeabccbaddddabccbaabccbaddddabccbaeefeffffffabccbaddddabccbaddbccbaaaabccbddfffffeeeeabccbaddddabcc… text/html 2026-09-27T02:10:20+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d120_4d432_d720_d840&rev=1790475020&do=diff This page demonstrates a permutation-fair d120 + 4d432 + d720 + d840 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. gggggggggggggggggggggggggggggggggggggggggfeabcddcbaeeeeecbaddabcedbaccabdeeeeeedbaccabdecbaddabceeeeeabcddcbaefffffecbaddabceeeeedbaccabdeabcddcbaeeeeeeabcddcbaedbaccabdeeeeecbaddabcefedbaccabdeeeeeabcddcbaecbaddabceeeeeecbaddabceabcddcbaeeeeedbaccabdeffffffedbaccabdeeeeeabcddcbaecbaddabceeeeeecbaddabceabcddcbaeeeeedbaccabdefecbaddabceeeeedbaccabdeabcddcbaee… text/html 2026-09-26T16:35:50+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d360_d504_d840_4d2520&rev=1790440550&do=diff This page demonstrates a permutation-fair d360 + d504 + d840 + 4d2520 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. With an LCM of 2520, this solution can be scaled to a homogeneous 7d2520. gggggggggggggggggggggggggggggggggggggggggfeffbacddcabcabddbacbacddcabdabccbadcabddbacdabccbaddabccbadeedabccbadcabddbacbacddcabcabddbacdabccbadbacddcabdabccbadfeffecabddbacbacddcabcabddbacbacddcabbacddcabcabddbacdabccbadefefcabddbacbacddcabbacddcabbacddcabdabccbadcabddbaccabddbacfffef… text/html 2026-09-26T13:41:40+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d360_d720_d840_4d5040&rev=1790430100&do=diff This page demonstrates a permutation-fair d360 + d720 + d840 + 4d5040 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. With an LCM of 5040, this solution can be scaled to a homogeneous 7d5040. gggggggggggggggggggggggggggggggggggggggggfeffbacddcabcabddbacbacddcabdabccbadcabddbacdabccbaddabccbadeedabccbadcabddbacbacddcabcabddbacdabccbadbacddcabdabccbadfeffecabddbacbacddcabcabddbacbacddcabbacddcabcabddbacdabccbadefefcabddbacbacddcabbacddcabbacddcabdabccbadcabddbaccabddbacfffe… text/html 2025-12-15T21:48:49+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d840_7d60480&rev=1765835329&do=diff This page demonstrates a go first fair d840+7d60480 configuration (with LCM of 60480), found by Paul Meyer on Dec 15, 2025. This was constructed by concatenating the 7d10080 set 6 times, and then inducing a d840 around the repetitions. hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggffffffffffffffffffabcdeedcbadcbeebcdaaaaecbddbceecbddbceaaaadcbeebcdabcdeedcbaaadcbeebcdabcdeedcbaaecdbbdceae… text/html 2026-09-27T02:11:57+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d840_d960_d1890_d2880_4d3456&rev=1790475117&do=diff This page demonstrates a permutation-fair d840 + d960 + d1890 + d2880 + 4d3456 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhgggggggggggfeabcddcbaeecbaddabcdbaccabdeeedbaccabdecbaddabceeeabcddcbafffffecbaddabceedbaccabdabcddcbaeeeabcddcbaedbaccabdeeecbaddabcfedbaccabdeeabcddcbacbaddabceeecbaddabceabcddcbaeeedbaccabdffffffdbaccabdeeeabcddcbaecbaddabceeecbaddabcabcddcbaeedbaccabdefcbaddabceeedbaccabdeabcddcbaeeeabcddcbadbaccabdeecba… text/html 2026-09-27T02:11:21+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d840_d1080_4d1728_d2880_d5040&rev=1790475081&do=diff This page demonstrates a permutation-fair d840 + d1080 + 4d1728 + d2880 + d5040 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhgggggggggggggggggggggggggggggggggggggggggffeabcddcbaeeeeecbaddabcedbaccabdeeeeeedbaccabdecbaddabceeeeeabcddcbaeffffffffffffeabcddcbaeeeeecbaddabcedbaccabdeeeeeedbaccabdecbaddabceeeeeabcddcbaeffeabcddcbaeeeeecbaddabcedbaccabdeeeeeedbaccabdecbaddabceeeeeabcddcbaeffffffffffffeabcddcbaeeeeecbaddabcedbaccabdeeee… text/html 2026-09-26T13:45:40+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d840_d1080_d1680_4d6048_d10080&rev=1790430340&do=diff This page demonstrates a permutation-fair d840 + d1080 + d1680 + 4d6048 + d10080 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. With an LCM of 30240, this solution can be scaled to a homogeneous 8d30240. hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhfeabcddcbaeeeeecbaddabcedbaccabdeeeeeedbaccabdecbaddabceeeeeabcddcbaefffffecbaddabceeeeedbaccabdeabcddcbaeeeeeeabcddcbaedbaccabdeeeeecbaddabcefedbaccabdeeeeeabcddcbaecbaddabceeeeeecbaddabceabcddcbaeeeeedbaccabdeffffffedbaccabdeeeee… text/html 2026-10-15T18:02:30+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d840_d1440_6d5040&rev=1792087350&do=diff This page demonstrates a permutation-fair d840 + d1440 + 6d5040 configuration of Go First Dice, found by Paul Meyer on Oct 15, 2026. With an LCM of 10080, this solution can be scaled to a homogeneous 8d10080. hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhggggggggefefeabcddcbadbaccabdfffdbaccabdeeffedbaccabdffcbaddabceeeeefecbaddabcfffabcddcbaeefefcbaddabcfffabcddcbaeeeeeefeeedbaccabdfffcbaddabceeeabcddcbaffcbaddabcfabcddcbafffffcbaddabceefeabcddcbafffffdbaccabdfeeecbaddabcabcddcbaeeeeeecbaddabcfffab… text/html 2026-09-26T16:46:21+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d840_d2160_d3024_d5040_4d15120&rev=1790441181&do=diff This page demonstrates a permutation-fair d840 + d1080 + d1680 + 5d15120 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. With an LCM of 15120, this solution can be scaled to a homogeneous 8d15120. hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhfffdabccbadcabddbacbacddcabfffefffbacddcabcabddbacdabccbadffffeffdabccbadcabddbacbacddcabefffffdabccbadcabddbacbacddcabffffbacddcabcabddbacdabccbadfffffffffffffbacddcabcabddbacdabccbadffefbacddcabcabddbacdabccbadfffffebacddcabcabddbacdabcc… text/html 2026-09-26T14:00:23+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d7200_d8400_d9072_d25200_4d25920_d43200&rev=1790431223&do=diff This page demonstrates a permutation-fair d7200 + d8400 + d9072 + d25200 + 4d25920 + d43200 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. With an LCM of 907200, this solution can be scaled to a homogeneous 9d907200. iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii… text/html 2026-09-26T17:13:07+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d7200_d8400_d9072_d25200_5d64800&rev=1790442787&do=diff This page demonstrates a permutation-fair d7200 + d8400 + d9072 + d25200 + 5d64800 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. With an LCM of 453600, this solution can be scaled to a homogeneous 9d453600. iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiihhhhh… text/html 2026-09-13T23:56:30+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d7560_d25920_d29160_d44800_d45360_4d46656&rev=1789343790&do=diff The d7560 + d25920 + d29160 + d44800 + d45360 + 4d46656 configuration was constructed via induction by concatenating the d840 + d2880 + d3240 + d5040 + 4d5184 set (E. Harshbarger/B. Hearn) 9 times, then inducing the final d44800. The final configuration is a bit too long to show here in entirety. text/html 2026-09-09T15:44:05+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d8400_d9072_7d604800&rev=1788968645&do=diff The d8400 + d9072 + 7d604800 configuration was constructed via induction by concatenating the d840 + 7d60480 set 10 times, then inducing the final d9072. The final configuration is a bit too long to show here in entirety. text/html 2026-09-27T02:14:17+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d8400_d9072_d9600_d18900_d28800_4d34560&rev=1790475257&do=diff This page demonstrates a permutation-fair d8400 + d9072 + d9600 + d18900 + d28800 + 4d34560 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhgggggggggggfeabcddcbaeecbaddabcdb… text/html 2026-09-27T02:12:47+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d8400_d9072_d10800_4d17280_d28800_d50400&rev=1790475167&do=diff This page demonstrates a permutation-fair d8400 + d9072 + d10800 + 4d17280 + d28800 + d50400 configuration of Go First Dice, found by Paul Meyer on Sept 26, 2026. iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhgggggggggggggggggggggggggggggggg… text/html 2026-09-13T23:56:51+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=d8400_d9072_d28800_d32400_d50400_4d51840&rev=1789343811&do=diff The d8400 + d9072 + d28800 + d32400 + d50400 + 4d51840 configuration was constructed via induction by concatenating the d840 + d2880 + d3240 + d5040 + 4d5184 set (E. Harshbarger/B. Hearn) 10 times, then inducing the final d9072. The final configuration is a bit too long to show here in entirety. text/html 2026-09-19T05:20:15+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=fairness&rev=1789795215&do=diff Concepts of Fairness Consider the following three “levels of fairness”, starting with the “weakest” (each stronger level of fairness actually implies the weaker levels): * Go-first-fair. This is as originally proposed by James Ernest to Eric Harshbarger. Each player has an equal chance of rolling the highest number, and that person would go first. text/html 2023-04-19T14:30:29+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=fast_perm_check&rev=1681914629&do=diff Fast-Perm-Check This algorithm was created by Landon Kryger to solve the problem of testing if a set of dice is permutation fair. If you have n players and s sides, the standard approach would require you to test every roll and would run in O(sn). This algorithm runs in approximately O( text/html 2023-03-02T17:39:11+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=history&rev=1677778751&do=diff History The concept of Go First Dice was first proposed to Eric Harshbarger during the summer of 2010 by James Ernest (founder of Cheapass Games). At the time James asked if Eric might be able to develop a set of dice (presumedly 6-sided) that would have “go first text/html 2026-09-19T05:27:59+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=homogeneous_solutions&rev=1789795679&do=diff Solution Counts For Homogeneous Sets These counts avoid equivalent sets where the dice are simply relabeled. In other words, these counts assume that in the string representation of a solution the first “a” appears before the first “b” which appears before the first “c”, and so on. text/html 2026-09-14T21:16:49+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=induction_and_cotesian_numbers&rev=1789420609&do=diff Note: The following explanation was largely AI-generated (via Gemini), and could likely benefit from additional manual verification by humans. Why the Induction Chart Diagonal Matches the Cotesian Numbers The diagonal numbers on the Go First Dice induction chart match the Cotesian numbers because constructing a fair ( text/html 2026-09-14T22:24:59+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=induction_chart&rev=1789424699&do=diff Induction Chart m copies of the original n-die set 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 24 30 n0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 text/html 2026-10-04T13:58:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=inhomogeneous_solutions&rev=1791122282&do=diff Solution Counts For Inhomogeneous Sets These are configuration counts for various inhomogeneous dice sets (as found via exhaustive computer search), either with mirror-symmetry or no such restriction (note that column-grouped and column-paired symmetry can only happen with homogeneous sets). These counts avoid equivalent sets where the dice are simply relabeled. In other words, these counts assume that, if a and b are equal sized dice, then in the string representation of a solution the first text/html 2023-03-02T17:38:56+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=introduction&rev=1677778736&do=diff Introduction “Go First Dice” are a set of dice that allows some number of players to each roll a different single die (picked arbitrarily from the set) and the following conditions hold: * There will never be ties. * Each possible ordering of the players (determined by highest result, next highest result, etc) has a mathematically equal chance of occurring. text/html 2023-02-26T16:54:10+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m2n2&rev=1677430450&do=diff 1+4+1 == 6 text/html 2023-02-26T17:44:03+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m2n3&rev=1677433443&do=diff 1+4+1 == 6 text/html 2023-02-26T16:56:50+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m3n2&rev=1677430610&do=diff 0+3+0+1 == 4 1+0+3+0 == 4 text/html 2023-02-26T17:44:49+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m3n3&rev=1677433489&do=diff 1+3+3+1 == 8 text/html 2023-02-26T16:57:46+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m4n2&rev=1677430666&do=diff 0+3+1+1+1 == 6 1+0+4+0+1 == 6 1+1+1+3+0 == 6 text/html 2023-02-26T17:45:28+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m4n3&rev=1677433528&do=diff 1+0+4+0+1 == 6 text/html 2023-02-26T18:01:23+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m4n4&rev=1677434483&do=diff 7+32+12+32+7 == 90 text/html 2023-03-02T15:23:04+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m4n5&rev=1677770584&do=diff 7+32+12+32+7 == 90 text/html 2023-02-26T16:59:37+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m5n2&rev=1677430777&do=diff 0+4+3+2+1+2 == 12 0+5+0+5+0+2 == 12 0+5+1+2+3+1 == 12 1+1+6+1+1+2 == 12 1+2+3+4+0+2 == 12 1+2+4+1+3+1 == 12 1+3+1+4+2+1 == 12 1+3+2+1+5+0 == 12 2+0+4+3+2+1 == 12 2+0+5+0+5+0 == 12 2+1+1+6+1+1 == 12 2+1+2+3+4+0 == 12 text/html 2023-02-26T17:46:09+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m5n3&rev=1677433569&do=diff 0+11+1+1+11+0 == 24 1+8+3+3+8+1 == 24 2+5+5+5+5+2 == 24 2+6+1+11+1+3 == 24 3+1+11+1+6+2 == 24 3+2+7+7+2+3 == 24 text/html 2023-02-27T15:16:24+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m5n4&rev=1677510984&do=diff 7+50+0+50+25+12 == 144 8+45+10+40+30+11 == 144 9+40+20+30+35+10 == 144 10+35+30+20+40+9 == 144 11+30+40+10+45+8 == 144 12+25+50+0+50+7 == 144 text/html 2023-03-02T15:23:41+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m5n5&rev=1677770621&do=diff 19+75+50+50+75+19 == 288 text/html 2023-02-26T17:00:28+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m6n2&rev=1677430828&do=diff 0+0+3+0+0+0+1 == 4 1+0+0+0+3+0+0 == 4 text/html 2023-02-26T17:46:51+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m6n3&rev=1677433611&do=diff 0+2+1+0+1+2+0 == 6 0+3+0+2+0+3+0 == 8 1+0+0+4+0+0+1 == 6 text/html 2023-02-27T15:33:42+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m6n4&rev=1677512022&do=diff 1+5+1+6+1+5+1 == 20 text/html 2023-03-02T15:24:37+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m6n5&rev=1677770677&do=diff 1+5+1+6+1+5+1 == 20 text/html 2024-04-17T15:31:46+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m6n6&rev=1713367906&do=diff 41+216+27+272+27+216+41 == 840 text/html 2026-09-14T15:15:29+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m6n7&rev=1789398929&do=diff 41+216+27+272+27+216+41 == 840 text/html 2023-02-26T17:03:45+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m7n2&rev=1677431025&do=diff 0+0+7+1+0+1+1+2 == 12 0+1+5+1+2+0+1+2 == 12 0+1+5+2+0+0+3+1 == 12 0+1+6+0+0+2+2+1 == 12 0+2+2+4+1+0+1+2 == 12 0+2+3+2+1+2+0+2 == 12 0+2+4+0+2+1+2+1 == 12 0+2+4+1+0+1+4+0 == 12 0+3+0+5+0+2+0+2 == 12 0+3+1+2+3+1+0+2 == 12 0+3+1+3+1+1+2+1 == 12 text/html 2023-02-26T17:53:49+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m7n3&rev=1677434029&do=diff 0+6+5+1+1+5+6+0 == 24 0+7+2+3+3+2+7+0 == 24 0+7+3+0+5+4+4+1 == 24 0+7+3+1+1+10+0+2 == 24 0+8+0+2+7+1+5+1 == 24 0+8+0+3+3+7+1+2 == 24 1+3+8+0+0+8+3+1 == 24 1+4+4+5+0+3+7+0 == 24 1+4+5+2+2+5+4+1 == 24 1+5+1+7+2+0+8+0 == 24 1+5+2+4+4+2+5+1 == 24 text/html 2024-01-16T00:52:58+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m7n4&rev=1705366378&do=diff 72+4+198+161+26+24+232+3 == 720 72+5+192+176+6+39+226+4 == 720 72+5+195+161+36+9+241+1 == 720 72+5+194+166+26+19+236+2 == 720 72+5+193+171+16+29+231+3 == 720 72+6+188+181+6+34+230+3 == 720 72+6+191+166+36+4+245+0 == 720 72+6+190+171+26+14+240+1 == 720 text/html 2023-03-03T13:09:46+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m7n5&rev=1677848986&do=diff 51+356+6+307+307+6+356+51 == 1440 52+351+15+302+302+15+351+52 == 1440 53+346+24+297+297+24+346+53 == 1440 54+341+33+292+292+33+341+54 == 1440 55+336+42+287+287+42+336+55 == 1440 56+331+51+282+282+51+331+56 == 1440 57+326+60+277+277+60+326+57 == 1440 text/html 2025-12-15T21:49:24+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m7n6&rev=1765835364&do=diff 41+216+27+272+27+216+41 == 840 text/html 2026-09-14T15:15:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m7n7&rev=1789398938&do=diff 751+3577+1323+2989+2989+1323+3577+751 == 17280 text/html 2023-02-26T17:04:40+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m8n2&rev=1677431080&do=diff 0+0+3+0+1+0+1+0+1 == 6 0+1+0+3+0+0+1+0+1 == 6 0+1+1+1+0+2+0+0+1 == 6 0+1+1+1+1+0+0+2+0 == 6 0+2+0+0+1+1+1+1+0 == 6 1+0+0+0+4+0+0+0+1 == 6 1+0+0+2+0+1+1+1+0 == 6 1+0+1+0+0+3+0+1+0 == 6 1+0+1+0+1+0+3+0+0 == 6 text/html 2023-02-26T17:54:42+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m8n3&rev=1677434082&do=diff 1+0+0+0+4+0+0+0+1 == 6 text/html 2024-01-15T23:00:50+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m8n4&rev=1705359650&do=diff 0+12+4+2+1+16+4+2+4 == 45 0+13+1+2+11+1+13+0+4 == 45 0+13+1+3+6+11+3+5+3 == 45 0+13+0+7+1+11+8+1+4 == 45 1+9+6+2+6+5+12+0+4 == 45 1+9+6+3+1+15+2+5+3 == 45 1+10+3+3+11+0+11+3+3 == 45 1+10+3+4+6+10+1+8+2 == 45 1+11+0+5+11+5+0+11+1 == 45 1+10+2+8+1+10+6+4+3 == 45 text/html 2023-03-02T15:22:19+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m8n5&rev=1677770539&do=diff 1+11+0+5+11+5+0+11+1 == 45 2+7+4+9+1+9+4+7+2 == 45 text/html 2026-09-14T15:13:07+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m8n6&rev=1789398787&do=diff 36+172+54+180+61+180+54+172+36 == 945 text/html 2026-09-14T15:15:46+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m8n7&rev=1789398946&do=diff 36+172+54+180+61+180+54+172+36 == 945 text/html 2023-02-26T17:05:32+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m9n2&rev=1677431132&do=diff 0+0+0+3+0+0+0+0+0+1 == 4 0+0+2+0+0+0+1+0+1+0 == 4 0+1+0+1+0+0+0+2+0+0 == 4 1+0+0+0+0+0+3+0+0+0 == 4 text/html 2023-02-26T17:56:54+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m9n3&rev=1677434214&do=diff 0+1+2+1+0+0+1+2+1+0 == 8 0+2+0+1+1+1+1+0+2+0 == 8 1+0+0+3+0+0+3+0+0+1 == 8 1+0+1+0+2+2+0+1+0+1 == 8 text/html 2024-01-15T23:02:41+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m9n4&rev=1705359761&do=diff 0+16+14+0+2+9+28+0+4+7 == 80 0+16+13+3+1+4+33+1+1+8 == 80 0+17+11+1+7+4+27+3+3+7 == 80 0+17+11+2+2+14+17+8+2+7 == 80 0+18+9+0+8+14+11+10+4+6 == 80 0+18+9+0+9+9+21+0+9+5 == 80 0+18+9+1+3+24+1+15+3+6 == 80 0+18+9+1+4+19+11+5+8+5 == 80 0+18+9+2+0+24+11+0+12+4 == 80 text/html 2023-03-02T17:45:19+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m9n5&rev=1677779119&do=diff 2+37+4+6+31+31+6+4+37+2 == 160 3+33+9+5+30+30+5+9+33+3 == 160 3+34+4+14+25+25+14+4+34+3 == 160 4+29+14+4+29+29+4+14+29+4 == 160 4+30+9+13+24+24+13+9+30+4 == 160 4+31+4+22+19+19+22+4+31+4 == 160 5+25+19+3+28+28+3+19+25+5 == 160 5+26+14+12+23+23+12+14+26+5 == 160 text/html 2026-09-14T15:13:17+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m9n6&rev=1789398797&do=diff 114+153+537+72+9+618+219+0+465+53 == 2240 text/html 2026-09-14T15:15:53+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m9n7&rev=1789398953&do=diff 141+800+17+1019+263+263+1019+17+800+141 == 4480 text/html 2026-09-14T15:17:52+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m9n8&rev=1789399072&do=diff 1443+7740+1062+8454+4716+1062+10890+18+8001+1414 == 44800 text/html 2023-02-26T17:07:52+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m10n2&rev=1677431272&do=diff 0+0+0+4+0+0+0+0+1+0+1 == 6 0+0+1+2+1+0+0+0+0+2+0 == 6 0+1+0+1+1+1+0+1+0+0+1 == 6 0+1+0+2+0+0+1+0+1+1+0 == 6 0+1+1+0+0+2+0+0+1+1+0 == 6 0+1+1+0+1+0+0+2+0+1+0 == 6 0+2+0+0+0+0+1+2+1+0+0 == 6 1+0+0+0+0+4+0+0+0+0+1 == 6 1+0+0+1+0+1+1+1+0+1+0 == 6 text/html 2023-02-26T17:57:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m10n3&rev=1677434258&do=diff 0+1+1+0+0+2+0+0+1+1+0 == 6 1+0+0+0+0+4+0+0+0+0+1 == 6 text/html 2024-01-15T23:04:13+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m10n4&rev=1705359853&do=diff 0+7+4+0+5+3+3+6+5+0+3 == 36 0+7+4+1+2+4+8+1+4+3+2 == 36 0+7+3+4+0+3+8+2+6+0+3 == 36 1+3+9+0+0+7+2+6+5+0+3 == 36 1+3+9+0+1+3+7+6+0+4+2 == 36 1+4+5+5+0+2+6+5+5+0+3 == 36 1+5+4+0+8+3+0+6+5+2+2 == 36 1+5+3+4+3+3+5+2+6+2+2 == 36 1+4+6+1+5+2+1+9+4+0+3 == 36 text/html 2023-03-02T15:28:20+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m10n5&rev=1677770900&do=diff 1+5+4+1+5+4+5+1+4+5+1 == 36 2+2+5+5+3+2+3+5+5+2+2 == 36 text/html 2024-04-17T14:22:48+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m10n6&rev=1713363768&do=diff The lowest K with palindromic solutions is 1512. Lower K values have not been ruled out for non-palindromic solutions. 41+251+2+268+169+50+169+268+2+251+41 == 1512 42+244+23+232+211+8+211+232+23+244+42 == 1512 42+245+15+260+155+78+155+260+15+245+42 == 1512 text/html 2026-09-14T15:16:01+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m10n7&rev=1789398961&do=diff 57+154+218+112+1+428+1+112+218+154+57 == 1512 text/html 2026-09-14T15:18:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m10n8&rev=1789399082&do=diff 263+1415+145+1780+160+1546+160+1780+145+1415+263 == 9072 text/html 2023-02-26T17:49:44+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m11n2&rev=1677433784&do=diff 0+0+0+5+3+0+0+1+0+0+1+2 == 12 0+0+0+6+1+0+2+0+0+0+1+2 == 12 0+0+0+7+0+0+0+2+0+1+0+2 == 12 0+0+0+7+0+0+1+0+1+0+2+1 == 12 0+0+1+4+1+2+1+0+0+0+1+2 == 12 0+0+1+4+2+1+0+0+1+1+0+2 == 12 0+0+1+5+0+2+0+0+1+0+2+1 == 12 0+0+1+5+1+0+0+1+2+0+0+2 == 12 0+0+1+5+1+0+0+2+0+0+2+1 == 12 text/html 2023-08-07T02:25:09+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m11n3&rev=1691375109&do=diff 0+0+10+0+0+2+0+1+7+1+3+0 == 24 0+0+10+0+1+0+0+2+8+1+1+1 == 24 0+0+9+1+2+0+0+2+1+9+0+0 == 24 0+0+9+2+0+0+1+3+1+7+1+0 == 24 0+1+8+0+1+2+2+1+0+8+1+0 == 24 0+1+7+1+3+1+0+0+2+9+0+0 == 24 0+1+8+0+2+0+2+1+5+2+3+0 == 24 0+1+8+0+2+1+0+0+9+1+1+1 == 24 text/html 2026-09-14T15:08:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m11n4&rev=1789398518&do=diff 39+47+70+37+153+37+34+41+104+58+80+20 == 720 text/html 2026-09-14T15:10:12+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m11n5&rev=1789398612&do=diff 5+303+5+6+387+14+14+387+6+5+303+5 == 1440 text/html 2026-09-14T15:13:26+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m11n6&rev=1789398806&do=diff 3316+154+15699+499+4599+54+16273+0+8265+0+10664+957 == 60480 text/html 2026-09-14T15:16:08+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m11n7&rev=1789398968&do=diff 3302+15478+10267+9+31421+3+3+31421+9+10267+15478+3302 == 120960 text/html 2026-09-14T15:18:14+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m11n8&rev=1789399094&do=diff 89907+547482+67+581329+423556+34+439396+601888+1+439924+393889+111327 == 3628800 text/html 2023-02-26T17:50:43+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m12n2&rev=1677433843&do=diff 0+0+0+0+3+0+0+0+0+0+0+0+1 == 4 1+0+0+0+0+0+0+0+3+0+0+0+0 == 4 text/html 2023-08-07T02:25:16+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m12n3&rev=1691375116&do=diff 0+0+2+0+1+0+0+0+1+0+2+0+0 == 6 1+0+0+0+0+0+4+0+0+0+0+0+1 == 6 0+1+1+0+0+1+1+1+0+0+1+1+0 == 7 0+0+3+0+0+0+2+0+0+0+3+0+0 == 8 1+0+0+0+3+0+0+0+3+0+0+0+1 == 8 0+1+1+1+1+0+1+0+1+1+1+1+0 == 9 0+1+2+0+0+0+1+2+1+1+0+0+1 == 9 0+2+0+0+1+0+3+0+1+0+0+2+0 == 9 text/html 2023-08-08T14:48:49+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m12n4&rev=1691506129&do=diff 0+4+0+1+1+5+1+0+0+5+1+1+1 == 20 1+0+5+0+1+0+6+0+1+0+5+0+1 == 20 1+1+1+5+0+0+1+5+1+1+0+4+0 == 20 text/html 2024-04-17T15:20:48+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m12n5&rev=1713367248&do=diff 1+0+5+0+1+0+6+0+1+0+5+0+1 == 20 0+8+0+2+3+7+4+1+0+9+0+5+1 == 40 1+5+1+6+1+5+2+5+1+6+1+5+1 == 40 2+0+10+0+2+0+12+0+2+0+10+0+2 == 40 1+5+0+9+0+1+4+7+3+2+0+8+0 == 40 0+9+3+0+5+7+2+7+5+0+3+9+0 == 50 0+10+0+1+9+5+0+5+9+1+0+10+0 == 50 0+9+2+4+1+3+12+3+1+4+2+9+0 == 50 text/html 2024-04-17T16:17:20+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m12n6&rev=1713370640&do=diff 5+26+13+6+42+0+26+0+42+6+13+26+5 == 210 6+21+21+5+33+6+26+6+33+5+21+21+6 == 210 7+16+29+4+24+12+26+12+24+4+29+16+7 == 210 8+11+37+3+15+18+26+18+15+3+37+11+8 == 210 8+12+31+16+7+4+54+4+7+16+31+12+8 == 210 9+6+45+2+6+24+26+24+6+2+45+6+9 == 210 text/html 2026-09-14T15:16:15+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m12n7&rev=1789398975&do=diff 5+26+13+6+42+0+26+0+42+6+13+26+5 == 210 text/html 2026-09-14T15:18:23+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m12n8&rev=1789399103&do=diff 56+230+175+78+282+204+50+204+282+78+175+230+56 == 2100 text/html 2023-02-27T15:17:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m13n2&rev=1677511026&do=diff 0+0+0+1+6+1+0+0+1+0+0+0+1+2 == 12 0+0+0+1+7+0+0+0+0+0+0+2+1+1 == 12 0+0+0+2+5+1+0+0+0+0+0+1+3+0 == 12 0+0+0+3+2+2+1+1+0+0+0+0+1+2 == 12 0+0+0+3+3+1+1+0+0+1+0+1+0+2 == 12 0+0+0+3+4+0+0+0+2+0+0+0+2+1 == 12 0+0+0+4+0+2+3+0+0+0+0+0+1+2 == 12 0+0+0+4+0+4+0+0+0+1+0+1+0+2 == 12 text/html 2023-08-08T14:42:57+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m13n3&rev=1691505777&do=diff 0+0+4+7+0+1+0+0+1+0+7+4+0+0 == 24 0+0+5+4+3+0+0+0+0+3+4+5+0+0 == 24 0+0+5+5+1+0+1+1+0+1+5+5+0+0 == 24 0+0+6+3+1+2+0+0+2+1+3+6+0+0 == 24 0+0+6+3+2+0+0+1+3+1+1+7+0+0 == 24 0+0+6+3+2+0+0+2+0+3+3+4+1+0 == 24 0+0+6+3+2+0+1+0+1+0+10+0+0+1 == 24 0+0+6+4+0+0+1+3+0+1+4+4+1+0 == 24 text/html 2026-09-14T15:08:58+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m13n4&rev=1789398538&do=diff 24+100+0+6+11+294+1+0+0+0+183+0+101+0 == 720 text/html 2026-09-14T15:10:48+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m13n5&rev=1789398648&do=diff 0+269+0+0+256+177+18+18+177+256+0+0+269+0 == 1440 text/html 2026-09-14T15:13:36+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m13n6&rev=1789398816&do=diff 2922+1044+9228+2735+8991+97+12+10971+2524+10503+0+58+11395+0 == 60480 text/html 2026-09-14T15:16:24+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m13n7&rev=1789398984&do=diff 2224+16348+5+16882+19+24997+5+5+24997+19+16882+5+16348+2224 == 120960 text/html 2026-09-14T15:18:32+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m13n8&rev=1789399112&do=diff 110245+240739+544489+70+91988+864700+4+46+678871+117+555435+12+468120+73964 == 3628800 text/html 2023-02-27T15:38:34+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m14n2&rev=1677512314&do=diff 0+0+0+1+1+2+0+0+0+0+0+1+0+0+1 == 6 0+0+0+2+0+1+1+0+0+0+0+0+1+1+0 == 6 0+0+0+2+1+0+0+0+0+2+0+0+0+0+1 == 6 0+0+0+3+0+0+0+0+0+0+1+1+1+0+0 == 6 0+0+1+0+0+3+0+0+0+0+0+0+1+1+0 == 6 0+0+1+1+0+1+0+0+1+0+0+1+0+1+0 == 6 0+0+1+1+1+0+0+0+0+0+0+3+0+0+0 == 6 text/html 2023-08-07T02:25:26+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m14n3&rev=1691375126&do=diff 0+1+0+0+1+1+0+0+0+1+1+0+0+1+0 == 6 1+0+0+0+0+0+0+4+0+0+0+0+0+0+1 == 6 0+0+1+4+1+0+0+0+0+0+1+4+1+0+0 == 12 0+0+2+3+0+0+0+2+0+0+0+3+2+0+0 == 12 0+0+2+3+0+0+1+0+0+1+1+3+0+1+0 == 12 0+1+0+3+1+1+0+0+1+0+0+3+2+0+0 == 12 0+1+0+4+0+0+0+0+3+0+0+2+1+1+0 == 12 text/html 2024-01-28T15:13:43+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m14n4&rev=1706454823&do=diff The lowest K with palindromic solutions is 180. There may still be non-palindromic solutions at K = 150. All other lower Ks have been ruled out. 12+0+11+21+24+13+3+12+3+13+24+21+11+0+12 == 180 12+0+11+22+20+17+7+2+7+17+20+22+11+0+12 == 180 12+0+11+24+11+31+0+2+0+31+11+24+11+0+12 == 180 text/html 2026-09-14T15:11:07+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m14n5&rev=1789398667&do=diff 5+12+18+14+8+11+3+38+3+11+8+14+18+12+5 == 180 text/html 2026-09-14T15:13:44+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m14n6&rev=1789398824&do=diff 47+0+223+0+84+8+154+48+154+8+84+0+223+0+47 == 1080 text/html 2026-09-14T15:16:34+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m14n7&rev=1789398994&do=diff 10+165+0+5+247+7+59+94+59+7+247+5+0+165+10 == 1080 text/html 2026-09-14T15:18:39+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m14n8&rev=1789399119&do=diff 536+4202+86+1820+6360+40+19+3352+5710+26+14+6044+2+3460+729 == 32400 text/html 2023-02-27T15:26:05+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m15n2&rev=1677511565&do=diff 0+0+0+0+0+3+0+0+0+0+0+0+0+0+0+1 == 4 0+0+1+0+0+0+1+0+1+0+0+0+0+0+1+0 == 4 0+1+0+0+0+0+0+1+0+1+0+0+0+1+0+0 == 4 1+0+0+0+0+0+0+0+0+0+3+0+0+0+0+0 == 4 text/html 2023-08-07T02:25:33+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m15n3&rev=1691375133&do=diff 0+0+1+1+2+0+0+0+0+0+0+2+1+1+0+0 == 8 0+0+2+0+1+0+1+0+0+1+0+1+0+2+0+0 == 8 0+1+0+1+0+2+0+0+0+0+2+0+1+0+1+0 == 8 0+1+0+1+1+0+0+1+1+0+0+1+1+0+1+0 == 8 0+1+1+0+0+0+1+1+1+1+0+0+0+1+1+0 == 8 0+1+1+0+0+1+0+0+1+1+2+0+0+0+0+1 == 8 1+0+0+0+0+2+1+1+0+0+1+0+0+1+1+0 == 8 text/html 2024-01-15T23:12:43+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m15n4&rev=1705360363&do=diff m11n3 has solutions for K=32, 48, 64, etc. K=32 solutions follow: 0+0+10+0+0+1+1+3+0+5+3+4+2+0+0+3 == 32 0+0+10+0+0+2+0+0+2+9+3+0+0+3+1+2 == 32 0+0+10+0+1+0+0+0+5+9+0+0+0+5+0+2 == 32 0+0+9+2+0+0+1+1+2+5+4+4+0+1+0+3 == 32 0+1+8+0+0+4+1+0+0+5+5+3+2+0+0+3 == 32 text/html 2026-09-14T15:11:23+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m15n5&rev=1789398683&do=diff 1+2+3+0+3+5+0+2+2+0+5+3+0+3+2+1 == 32 text/html 2026-09-14T15:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m15n6&rev=1789398834&do=diff 26+158+5+7+323+59+10+0+7+398+4+17+120+1+209+0 == 1344 text/html 2026-09-14T15:16:42+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m15n7&rev=1789399002&do=diff 15+405+0+1+508+49+302+64+64+302+49+508+1+0+405+15 == 2688 text/html 2026-09-14T15:18:48+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m15n8&rev=1789399128&do=diff 70+665+145+41+730+744+0+30+48+1495+31+35+0+1136+0+206 == 5376 text/html 2023-08-07T01:26:30+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m16n2&rev=1691371590&do=diff 0+1+1+0+0+0+0+0+0+0+0+3+1+0+0+0+0 == 6 0+0+2+0+0+0+0+0+1+0+1+0+1+0+1+0+0 == 6 0+1+0+0+0+0+1+2+0+0+0+1+0+0+0+0+1 == 6 0+1+0+0+0+1+0+1+0+1+1+0+0+0+0+0+1 == 6 0+1+0+0+0+1+1+0+0+1+0+0+1+0+0+1+0 == 6 0+1+0+0+0+2+0+0+0+0+0+1+1+0+1+0+0 == 6 0+1+0+0+1+0+0+1+0+0+1+1+0+0+0+1+0 == 6 text/html 2023-08-07T02:29:29+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m16n3&rev=1691375369&do=diff 1+0+0+0+0+0+0+0+4+0+0+0+0+0+0+0+1 == 6 0+1+0+2+0+0+0+1+0+1+0+3+0+0+0+0+1 == 9 1+0+0+0+0+3+0+1+0+1+0+0+0+2+0+1+0 == 9 1+0+0+0+2+0+0+0+3+0+0+0+2+0+0+0+1 == 9 text/html 2024-01-15T23:32:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m16n4&rev=1705361522&do=diff 0+6+2+0+4+5+0+5+1+5+0+5+4+0+2+6+0 == 45 0+5+2+6+0+1+0+4+9+4+0+1+0+6+2+5+0 == 45 0+6+1+3+2+4+1+3+5+3+1+4+2+3+1+6+0 == 45 0+6+0+6+0+3+2+1+9+1+2+3+0+6+0+6+0 == 45 0+7+0+0+4+7+2+2+1+2+2+7+4+0+0+7+0 == 45 1+0+11+0+0+0+5+0+11+0+5+0+0+0+11+0+1 == 45 1+3+2+7+0+2+0+4+7+4+0+2+0+7+2+3+1 == 45 text/html 2026-09-14T15:11:52+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m16n5&rev=1789398712&do=diff 0+6+0+6+0+3+2+1+9+1+2+3+0+6+0+6+0 == 45 text/html 2026-09-14T15:14:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m16n6&rev=1789398842&do=diff 0+146+1+0+87+156+19+18+91+18+19+156+87+0+1+146+0 == 945 text/html 2026-09-14T15:16:51+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m16n7&rev=1789399011&do=diff 0+140+21+0+18+232+19+12+61+12+19+232+18+0+21+140+0 == 945 text/html 2026-09-14T15:18:58+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m16n8&rev=1789399138&do=diff 534+10+2393+753+0+177+1383+2844+1+4+15+1937+2068+1+1+1954+100 == 14175 text/html 2023-08-07T02:24:17+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m18n2&rev=1691375057&do=diff 1+0+0+0+0+0+0+0+0+0+0+0+3+0+0+0+0+0+0 == 4 0+0+0+0+0+0+3+0+0+0+0+0+0+0+0+0+0+0+1 == 4 0+0+0+0+2+0+0+0+0+0+0+0+1+0+0+0+1+0+0 == 4 0+0+1+0+0+0+1+0+0+0+0+0+0+0+2+0+0+0+0 == 4 1+0+0+0+0+0+0+0+0+4+0+0+0+0+0+0+0+0+1 == 6 1+0+0+0+0+0+0+2+0+0+1+0+0+0+0+2+0+0+0 == 6 text/html 2023-08-08T14:21:21+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m18n3&rev=1691504481&do=diff 0+0+0+2+0+0+1+0+0+0+0+0+1+0+0+2+0+0+0 == 6 0+0+1+0+0+2+0+0+0+0+0+0+0+2+0+0+1+0+0 == 6 0+1+0+0+0+1+0+0+1+0+1+0+0+1+0+0+0+1+0 == 6 1+0+0+0+0+0+0+0+0+4+0+0+0+0+0+0+0+0+1 == 6 0+0+0+3+0+0+0+0+0+2+0+0+0+0+0+3+0+0+0 == 8 0+0+1+0+2+0+1+0+0+0+0+0+1+0+2+0+1+0+0 == 8 text/html 2023-08-08T17:09:06+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m18n4&rev=1691514546&do=diff 0+3+0+0+0+4+0+3+0+0+1+2+1+1+1+1+1+2+0 == 20 0+2+1+1+1+1+1+2+1+0+0+3+0+4+0+0+0+3+0 == 20 1+0+0+5+0+0+1+0+0+6+0+0+1+0+0+5+0+0+1 == 20 text/html 2026-09-14T15:12:03+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m18n5&rev=1789398723&do=diff 1+0+0+5+0+0+1+0+0+6+0+0+1+0+0+5+0+0+1 == 20 text/html 2026-09-14T15:14:12+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m18n6&rev=1789398852&do=diff 0+37+0+16+4+23+35+12+5+16+5+12+35+23+4+16+0+37+0 == 280 text/html 2026-09-14T15:17:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m18n7&rev=1789399020&do=diff 9+12+2+52+0+5+25+0+8+54+8+0+25+5+0+52+2+12+9 == 280 text/html 2026-09-14T15:19:07+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m18n8&rev=1789399147&do=diff 29+291+42+138+94+447+2+12+278+186+0+366+0+347+0+4+471+1+92 == 2800 text/html 2023-08-07T02:24:37+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m20n2&rev=1691375077&do=diff 0+0+2+0+0+0+0+0+0+0+0+0+1+0+2+0+1+0+0+0+0 == 6 1+0+0+0+0+0+0+0+0+0+4+0+0+0+0+0+0+0+0+0+1 == 6 1+0+0+0+0+0+0+0+0+3+0+0+0+0+1+0+0+0+0+1+0 == 6 0+1+0+0+0+0+0+1+0+1+1+0+0+1+0+0+0+0+0+0+1 == 6 0+1+0+0+0+0+0+1+1+0+1+0+0+0+0+1+0+0+0+1+0 == 6 0+1+0+0+0+0+0+2+0+0+0+0+1+0+1+0+0+0+0+1+0 == 6 text/html 2023-08-08T14:23:20+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m20n3&rev=1691504600&do=diff 0+0+1+0+1+0+0+0+0+0+2+0+0+0+0+0+1+0+1+0+0 == 6 1+0+0+0+0+0+0+0+0+0+4+0+0+0+0+0+0+0+0+0+1 == 6 0+0+0+2+1+0+1+0+0+0+1+0+0+0+1+0+1+2+0+0+0 == 9 0+0+1+0+1+2+0+0+0+0+1+0+0+0+0+2+1+0+1+0+0 == 9 0+0+1+0+2+0+1+0+0+0+0+1+0+1+0+1+0+1+1+0+0 == 9 0+0+1+1+0+1+0+1+0+1+0+0+0+0+1+0+2+0+1+0+0 == 9 text/html 2024-01-15T23:34:13+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m20n4&rev=1705361653&do=diff 0+4+0+3+0+3+2+2+0+4+0+4+0+2+2+3+0+3+0+4+0 == 36 1+0+5+0+4+0+1+0+5+0+4+0+5+0+1+0+4+0+5+0+1 == 36 2+0+2+0+5+0+5+0+3+0+2+0+3+0+5+0+5+0+2+0+2 == 36 text/html 2026-09-14T15:12:18+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m20n5&rev=1789398738&do=diff 1+0+5+0+4+0+1+0+5+0+4+0+5+0+1+0+4+0+5+0+1 == 36 text/html 2026-09-14T15:14:22+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m20n6&rev=1789398862&do=diff 3+35+13+1+24+46+6+14+12+0+70+0+12+14+6+46+24+1+13+35+3 == 378 text/html 2026-09-14T15:17:10+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m20n7&rev=1789399030&do=diff 0+46+2+0+26+48+16+0+13+2+72+2+13+0+16+48+26+0+2+46+0 == 378 text/html 2026-09-14T15:19:14+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m20n8&rev=1789399154&do=diff 27+209+1+73+265+158+18+35+2+259+345+20+0+0+20+487+53+14+0+281+1 == 2268 text/html 2023-08-07T02:24:47+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m24n2&rev=1691375087&do=diff 0+0+0+0+0+0+0+0+3+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+1 == 4 1+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+3+0+0+0+0+0+0+0+0 == 4 0+0+0+0+0+1+1+0+0+1+0+0+0+0+0+0+0+1+0+0+0+0+0+1+0 == 5 0+0+0+0+1+0+1+0+0+0+1+0+0+0+0+0+0+0+1+0+0+0+1+0+0 == 5 0+0+0+1+0+0+0+1+0+0+1+0+0+0+0+0+0+0+0+1+0+1+0+0+0 == 5 text/html 2023-08-08T14:25:02+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m24n3&rev=1691504702&do=diff 1+0+0+0+0+0+0+0+0+0+0+0+4+0+0+0+0+0+0+0+0+0+0+0+1 == 6 0+0+0+0+2+0+0+0+1+0+0+0+0+0+0+0+1+0+0+0+2+0+0+0+0 == 6 0+0+1+0+1+0+0+0+0+0+1+0+1+0+1+0+0+0+0+0+1+0+1+0+0 == 7 1+0+0+0+0+0+0+0+3+0+0+0+0+0+0+0+3+0+0+0+0+0+0+0+1 == 8 0+0+0+0+3+0+0+0+0+0+0+0+2+0+0+0+0+0+0+0+3+0+0+0+0 == 8 text/html 2024-01-15T23:27:19+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m24n4&rev=1705361239&do=diff m20n4 has solutions for K=20, 25, 30, etc. Solutions for K=20 follow. 0+0+4+0+0+0+1+0+1+0+5+0+1+0+0+0+0+0+5+0+1+0+1+0+1 == 20 0+2+1+0+0+0+1+2+1+3+0+1+0+0+0+1+0+3+0+2+0+2+0+0+1 == 20 0+2+1+0+0+1+0+1+0+6+0+0+0+0+0+0+2+3+0+0+0+2+1+1+0 == 20 0+2+1+0+0+1+0+2+0+3+0+1+2+0+1+0+0+1+0+2+0+3+0+1+0 == 20 text/html 2026-09-14T15:12:28+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m24n5&rev=1789398748&do=diff 1+0+0+0+5+0+0+0+1+0+0+0+6+0+0+0+1+0+0+0+5+0+0+0+1 == 20 text/html 2026-09-14T15:14:38+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m24n6&rev=1789398878&do=diff 0+10+1+4+1+7+9+2+3+6+0+3+13+3+0+6+3+2+9+7+1+4+1+10+0 == 105 text/html 2026-09-14T15:17:21+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m24n7&rev=1789399041&do=diff 2+4+3+11+0+1+4+11+3+3+3+2+11+2+3+3+3+11+4+1+0+11+3+4+2 == 105 text/html 2026-09-14T15:19:22+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m24n8&rev=1789399162&do=diff 3+100+2+3+103+36+33+92+4+10+53+15+142+15+53+10+4+92+33+36+103+3+2+100+3 == 1050 text/html 2023-08-07T02:25:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m30n2&rev=1691375100&do=diff 0+0+0+0+0+0+0+0+0+0+3+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+1 == 4 0+0+0+0+1+0+0+0+0+0+0+0+1+0+0+0+1+0+0+0+0+0+0+0+0+0+0+0+1+0+0 == 4 0+0+1+0+0+0+0+0+0+0+0+0+0+0+1+0+0+0+1+0+0+0+0+0+0+0+1+0+0+0+0 == 4 1+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+3+0+0+0+0+0+0+0+0+0+0 == 4 text/html 2023-08-08T14:27:48+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m30n3&rev=1691504868&do=diff 0+0+0+0+0+2+0+0+0+0+1+0+0+0+0+0+0+0+0+0+1+0+0+0+0+2+0+0+0+0+0 == 6 0+0+0+0+1+1+0+0+0+0+0+0+0+1+0+0+0+1+0+0+0+0+0+0+0+1+1+0+0+0+0 == 6 0+0+0+1+0+0+1+0+0+0+0+0+0+0+0+2+0+0+0+0+0+0+0+0+1+0+0+1+0+0+0 == 6 0+1+0+0+0+0+0+0+0+0+1+0+0+1+0+0+0+1+0+0+1+0+0+0+0+0+0+0+0+1+0 == 6 text/html 2023-09-18T01:51:59+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m30n4&rev=1695001919&do=diff 0+0+0+3+0+3+0+0+0+1+0+0+0+2+0+0+1+0+0+3+1+3+0+0+0+0+1+0+0+1+1 == 20 0+0+0+3+1+2+0+0+0+0+0+0+0+2+1+2+1+0+0+1+0+3+0+0+0+1+1+0+0+2+0 == 20 0+0+0+4+0+0+0+3+0+0+0+0+1+0+0+0+0+4+1+2+0+0+1+0+1+0+0+1+0+2+0 == 20 0+0+0+4+0+1+0+0+0+1+1+2+0+0+0+0+1+0+0+3+1+2+0+1+0+1+0+0+0+1+1 == 20 0+0+0+4+0+1+0+0+0+2+1+0+0+0+0+0+0+5+0+2+0+0+0+0+1+2+0+0+1+0+1 == 20 0+0+0+4+0+1+0+1+0+0+1+0+0+0+1+2+0+3+0+2+0+0+0+0+1+1+0+1+1+1+0 == 20 0+0+0+4+1+0+0+0+0+0+0+4+0+0+0+0+1+1+1+3+0+0+1+0+0+0+0+3+0+1+0 == 20 0+0+0+4+1+0+0+0+0+0+1+2+… text/html 2026-09-14T15:12:39+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m30n5&rev=1789398759&do=diff 1+0+0+0+0+5+0+0+0+0+1+0+0+0+0+6+0+0+0+0+1+0+0+0+0+5+0+0+0+0+1 == 20 text/html 2026-09-14T15:15:00+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m30n6&rev=1789398900&do=diff 5+1+8+5+1+0+31+1+1+0+0+8+2+3+4+28+4+3+2+8+0+0+1+1+31+0+1+5+8+1+5 == 168 text/html 2026-09-14T15:17:29+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m30n7&rev=1789399049&do=diff 0+13+4+0+2+1+23+9+1+5+1+1+0+1+21+4+21+1+0+1+1+5+1+9+23+1+2+0+4+13+0 == 168 text/html 2026-09-14T15:19:31+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=m30n8&rev=1789399171&do=diff 6+9+3+37+0+2+1+30+7+22+1+8+12+11+10+18+10+11+12+8+1+22+7+30+1+2+0+37+3+9+6 == 336 text/html 2026-09-17T22:46:01+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=more_info&rev=1789685161&do=diff More Information Where You Can Buy Go First Dice * U.S.: The Dice Shop at MathArtFun * U.K.: MathsGear Publications * 2012 article in The Guardian * GAMES MAGAZINE, December 2012. Much like the newspaper article above, this one is very much not math-focused; it is meant to introduce the concept of Go First Dice to laypeople. * text/html 2023-03-25T19:01:20+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=no_problem&rev=1679770880&do=diff A Solution Looking For A Problem In an attempt to deflect emails and other correspondence from people who are wondering what the point of all of this is, let me (Eric) state upfront: I understand that there are plenty of ways to quickly determine who goes first in a game. text/html 2026-09-19T05:23:19+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=open_questions&rev=1789795399&do=diff Open Questions 5d30? The most obvious question is whether or not a permutation fair 5d30 set exists. If such a set exists, it would make a beautiful successor to the 4d12 set that is commercially available. If such a set does not exist, it would be nice to have a proof of that (whether a mathematical proof or via exhaustive computer search). We already know (via exhaustive computer search) that a column-grouped 5d30 set can not be all-subset-place-fair, much less perm-fair. This also rules out… text/html 2024-03-09T22:30:09+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=participants&rev=1710023409&do=diff Wiki Participants Eric Harshbarger Eric Harshbarger did not first ask the question about the existence of Go First Dice; rather he was the first asked about them (by game-designer friend James Ernest in 2010). He and friend Robert Ford soon discovered early results. Over the next decade Eric continued intermittent research on the topic, and has served as an organizer and curator of the results obtained by himself and others who have been interested in the topic. text/html 2026-10-15T18:00:18+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=records&rev=1792087218&do=diff Current Records Here is a chart summarizing the best/smallest sets known for various player counts. Entries are known to be the best (lowest) possible values achievable (generally through exhaustive computer search). Players Smallest LCM (all dice same size) text/html 2026-09-19T05:15:25+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=significant_solutions&rev=1789794925&do=diff Significant Solutions Below is a (more or less) chronological listing of some of the most important Go First Dice sets that have been discovered and brief explanations about their significance. 3d6 acbbacbccaabacbbac Discovered by Robert Ford (on 10 August 2010). May not have been the first such set; Eric Harshbarger remembers hearsay that a three player set had been sold previously text/html 2023-08-02T22:12:32+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=start&rev=1691014352&do=diff Go First Dice Wiki This wiki serves as a repository the active research about “Go First Dice”. As it will likely be authored by more individuals than Eric Harshbarger alone, the information should be more current, accurate, and inclusive than that which is available on text/html 2023-02-27T17:36:13+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=supercomputer&rev=1677519373&do=diff A Supercomputer Joins The Search In February of 2023 Eric Harshbarger started using resources at the Alabama Supercomputer Authority to search certain spaces for possible permutation-fair sets. The hope is that such improved speeds will help fill in entries farther down the list on the page of text/html 2024-01-28T21:58:55+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=terminology&rev=1706479135&do=diff Terminology * Alphabetic String. An alphabetic string (or just “string”) is a representation of a dice set that is more convenient than the traditional “array listing” and takes advantage of the fact that it is assumed that no numeric values are repeated across the dice. In an alphabetic string of text/html 2023-05-15T16:33:33+00:00 Anonymous (anonymous@undisclosed.example.com) http://www.ericharshbarger.org/wiki/doku.php?id=weave_method&rev=1684168413&do=diff [The text below was originally composed by Landon Kryger when he was first developing ideas to create a program to search dice spaces for permutation-fair solutions.] Introduction The basic idea of the weave method is that you can't have a set of 4 fair dice, unless every 3 dice subset is also fair. You start with a n=0 dice set and doing a depth first search, you add one die at a time.