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--- significant_solutions [2024/02/20 11:13]
jamesgrime
+++ significant_solutions [2026/09/19 05:15] (current)
bmenrigh added 6d30 place-fair solution
@@ Line 22: / Line 22: @@
 Discovered by Eric Harshbarger (who used the fewest-sides-known 4-player set and "induced" a 5-player set from it using Paul Vanetti's method). The d72 in this set is //nearly// suitable for a physical die.
+===6d30 (place-fair)===
+**''abcdeffdebcafeacdbcebdafdebafccbfdeafcadbeabdfecaecdbfacfdbefbedcabecdfadefabceabcfdafdcbeebcdfadfcbaecbafedafdcebacdebfebdfcafbdceacefdbaebdacfaedfbccfabedfadbecbdcaefacbedffedcba''**
+Discovered by Brandon Enright in September 2026. This set uses column-grouping and was found by computer search. For column-grouping this solution is, in some sense, optimal. There are no column-grouped 5d30 or 6d30 sets that are permutation fair, or even place-fair for all subsets. Whether a non-column-grouped 5 or 6 30-sided set exist with permutation fairness or all-subset-place-fair is still an open question.
 ===5d60 (place-fair)===

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