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significant_solutions [2023/04/18 16:43]
harshec |
significant_solutions [2026/09/19 05:15] (current)
bmenrigh added 6d30 place-fair solution |
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| 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. | 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. |
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| | ===6d30 (place-fair)=== |
| | **''abcdeffdebcafeacdbcebdafdebafccbfdeafcadbeabdfecaecdbfacfdbefbedcabecdfadefabceabcfdafdcbeebcdfadfcbaecbafedafdcebacdebfebdfcafbdceacefdbaebdacfaedfbccfabedfadbecbdcaefacbedffedcba''** |
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| | 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. |
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| ===5d60 (place-fair)=== | ===5d60 (place-fair)=== |
| **''eabcddbacecabdeedabcdcbaeecbadcabdeebacddcbaeecbadcbadeedbacedabcdabceedabcdcabeecabddbacecabdeebacddcabeedbacdbacedabceeabcdeabcdecabdcbadeebacddcabeecabddcbaeecbaddabcecbadecbadeecabdebacddcbaeedbacdabceebacdedbacdabceecbadcabdeedabcdcabedbaceecabddbaceeabcddcabeecbadcabdeedabcdcbaeedbaceabcdcbade''** | **''eabcddbacecabdeedabcdcbaeecbadcabdeebacddcbaeecbadcbadeedbacedabcdabceedabcdcabeecabddbacecabdeebacddcabeedbacdbacedabceeabcdeabcdecabdcbadeebacddcabeecabddcbaeecbaddabcecbadecbadeecabdebacddcbaeedbacdabceebacdedbacdabceecbadcabdeedabcdcabedbaceecabddbaceeabcddcabeecbadcabdeedabcdcbaeedbaceabcdcbade''** |
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| Discovered by James Grime and Brian Pollock in 2014. This set of five 60-sided dice is "place fair" but not "permutation fair" (though it is tantalizingly close to exhibiting that stronger fairness). It was constructed using an original technique that Grime and Pollock call "binary construction". | Discovered by James Grime and Brian Pollock (on 29 November 2015). This set of five 60-sided dice is "place fair" but not "permutation fair" (though it is tantalizingly close to exhibiting that stronger fairness). It was constructed using an original technique that Grime and Pollock call "binary construction". |
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| | ===5d30 (place-fair)=== |
| | **''dbeaceacbdcabdedcbeaacdbeebcadedbacabcedacedbbdecacebdadbaecedacbdcaebbadcedecbabcaedacebdeadbccdebabadceaedbcbcaedcbedaedabcaecdbdcbeabdceacadbeeabdc''** |
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| | Discovered by Brandon Enright (2012). This set of five 30-sided dice is "place fair". This shows that we cannot prove that a set of 5d30 permutation-fair dice is impossible via Go-First-fairness or place-fairness. |
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| ===d20+d36+2d48+d54=== | ===d20+d36+2d48+d54=== |
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| ===5d120=== | ===5d120=== |
| Discovered by Mike Purcell (on 12 December 2022). This set lowered the size of a 5-player homogeneous set to 120 sides. It can be physically produced as there is [[https://en.wikipedia.org/wiki/Disdyakis_triacontahedron|an isohedral 120-sided geometric solid]]. | **''eeacbddbcabcdaadcbdcabbacdeeeeeeeedcabbacdbcdaadcbacbddbcaeeeedcbaabcdbcaddacbacdbbdcaeeeeeeeeacdbbdcabcaddacbdcbaabcdeeaaecbddbcebcdeedcbdcebbecdaaaaaaaadcebbecdbcdeedcbecbddbceaaaadcbeebcdbceddecbecdbbdceaaaaaaaaecdbbdcebceddecbdcbeebcdaaddecabbaceacbeebcabceaaecbddddddddbceaaecbacbeebcaecabbaceddddbcaeeacbacebbecaecbaabceddddddddecbaabceacebbecabcaeeacbddbbecaddaceacdeedcadceaaecdbbbbbbbbdceaaecdacdeedcaecaddacebbbbdcaeeacdaceddecaecdaadcebbbbbbbbecdaadceaceddecadcaeeacdbbccaedbbdeadebaabedbeaddaebccccccccbeaddaebdebaabedaedbbdeaccccbedaadebdeabbaedaebddbeaccccccccaebddbeadeabbaedbedaadebcc''** |
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| | Discovered by Mike Purcell (on 12 December 2022). This set lowered the size of a 5-player homogeneous set to 120 sides. It can be physically produced as there is [[https://en.wikipedia.org/wiki/Disdyakis_triacontahedron|an isohedral 120-sided geometric solid]]. This set was produced by [[https://flyinghorseduck.com/|Flying Horseduck]] in a very limited run. |
| | {{:flyinghorseduck_5d120.png?400|}}{{::flyinghorseduck_5d120wcase.png?400|}} |
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| ===d20+4d36=== | ===d20+4d36=== |
| **''ecbdaadbcabcddcbadbaccabdeeeeedbaccabdcbdaadbcabcddcbaeabcddcbadbaccabdcbdaadbceeeeeeabcddcbadbaccabdcbdaadbcedbaccabdcbdaadbcabcddcbaeeeeecbdaadbcabcddcbadbaccabde''** | **''ecbdaadbcabcddcbadbaccabdeeeeedbaccabdcbdaadbcabcddcbaeabcddcbadbaccabdcbdaadbceeeeeeabcddcbadbaccabdcbdaadbcedbaccabdcbdaadbcabcddcbaeeeeecbdaadbcabcddcbadbaccabde''** |
| {{ bram-set.jpg?200}} | {{ wiki:bram-set.jpg?200}} |
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| Discovered by Bram Cohen (on 26 December 2022). This set currently holds the records for the 'fewest total sides" and the "smallest largest die" in the set. | Discovered by Bram Cohen (on 26 December 2022). This set currently holds the records for the 'fewest total sides" and the "smallest largest die" in the set. |
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| | ===5d60=== |
| | **''abcdeedcbadcbeebcdaaaaecbddbceecbddbceaaaadcbeebcdabcdeedcbaaadcbeebcdabcdeedcbaaecdbbdceaecdbbdceaabcdeedcbadcbeebcdaaaaaaecbddbceaabceddecbdcebbecdaadcebbecdbceddecbaaecbddbceaaaaaadcebbecdaecdbbdceaabcdeedcbabcdeedcbaaecdbbdceadcebbecdaaaecbddbceabceddecbaaaadcebbecddcebbecdaaaabceddecbaecbddbcea''** |
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| | {{ :gofirstdice_5d60.png?400|}}Discovered by Paul Meyer (on 31 July 2023). This set improves upon Michael Purcell's 5d120 set by reducing the number of sides in a five player homogeneous set. Image rendered by Carl Hoff. |
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