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Here is a chart summarizing the best/smallest sets known for various player counts. Entries in red are known to be the best (lowest) possible values achievable (generally through exhaustive computer search).

Players Smallest LCM Fewest Total Sides Smallest Largest Die Smallest “Nice”* Set
2 2 (2d2) 3 (aba) 2 (aba) 2d4
3 6 (3d6)
R. Ford
12 (d2+d4+d6) 6 (various) 2d4+d6
4 12 (4d12)
R. Ford
30 (d4+d6+d8+d12)
E. Harshbarger
9 (d6+2d8+d9)
E. Harshbarger
d4+d6+d8+d12
5 60 (5d60)
P. Meyer
164 (d20+4d36)
B. Cohen
36 (d20+4d36)
B. Cohen
4d48_d30
P. Meyer
6 360 (d20+5d360, d36+5d360)
M. Purcell
746 (d80+d90+4d144)
E. Harshbarger
144 (d80+d90+4d144)
E. Harshbarger
?
7 ? 5316 (d480+d540+d840+4d864)
E. Harshbarger
864 (d480+d540+d840+4d864)
E. Harshbarger
?
8 ? 32736 (d840+d2880+d3240+d5040+4d5184)
E. Harshbarger/B. Hearn
5184 (d840+d2880+d3240+d5040+4d5184)
E. Harshbarger/B. Hearn
?
9 ? 3844224 (d7560 + d25920 + d29160 + d45360 + 4d46656 + d89600)
B. Hearn
89600 (d7560 + d25920 + d29160 + d45360 + 4d46656 + d89600)
B. Hearn
?

* A “nice” set comprises dice that are all isohedral shapes that are not lenses or rolling logs (“nice” is definitely subjective, since 2n-lens-shaped dice with small n values are definitely functional and pleasing enough for some folks' tastes). Also, a d2 (a coin) is not considered “nice”, but that is purely the opinion of this author (Eric).

records.1706478217.txt.gz · Last modified: 2024/01/28 21:43 by harshec