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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 |
| 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 2<i>n</i>-lens-shaped dice with small <i>n</i> values are definitely function and pleasing enough some some folks tastes. Also, a d2 (a coin) is not considered “nice”, but that is purely the opinion of this author (Eric).
records.1706477718.txt.gz · Last modified: 2024/01/28 21:35 by harshec
