Talk:Sicherman dice

Are there any Sicherman Dices for Other N-Side Dices?

The mathematical justification tells that it's also possible to extend it into other Dices. So what are the other Sicherman Dices? for D8 for D20 Supyovalk (talk) 09:42, 27 September 2023 (UTC)

You can split $(x+x^{2}+...+x^{8})^{2}$ into factors $(x(x+1)(x^{2}+1)(x^{4}+1))^{2}$ and arrange these non-traditionally, e.g. $(x(x+1)(x^{2}+1)^{2})(x(x+1)(x^{4}+1)^{2})$ with $x(x+1)(x^{2}+1)^{2}=x+x^{2}+2x^{3}+2x^{4}+x^{5}+x^{6}$ and $x(x+1)(x^{4}+1)^{2}=x+x^{2}+2x^{5}+2x^{6}+x^{9}+x^{10}$, thus producing the labelings 1,2,3,3,4,4,5,6 and 1,2,5,5,6,6,9,10. Other non-traditional arrangements lead to 1,2,2,3,5,6,6,7 and 1,3,3,5,5,7,7,9 or 1,2,2,3,3,4,4,5 and 1,3,5,5,7,7,9,11.

2003:DF:770D:1D00:41D1:3C1F:9358:DB4D (talk) 13:24, 15 August 2024 (UTC)