Jekyll2026-09-19T21:07:06+00:00http://sam.stromwall.org/feed.xmlSam Stromwall’s BlogSam StromwallThe Only Post2026-09-18T00:00:00+00:002026-09-18T00:00:00+00:00http://sam.stromwall.org/2026/09/18/initial-postThis blog is under construction. I have no content to give you, so here’s a numbers fact.

A typical $20$-sided die is numbered from $1$ to $20$, so the sum of all its faces is $210$. If I gave you a blank die and asked you to write a non-negative integer on each face so that your die also sums to $210$, then there are $43 674 337 807 412 863 662 664 548$ distinct dice you could produce. That would be the coefficient on $z^{210}$ in the Taylor expansion of this rational function.

\[\frac1{60(1-z)^{20}} + \frac1{3(1-z)^2(1-z^3)^6} + \frac1{4(1-z^2)^{10}} + \frac2{5(1-z^5)^4}\]]]>["Sam Stromwall"]