Earlier today I calculated the number of distinct states for the Petaminx (

see this post) and since I was already more than halfway to a general formula for any N-minx I figured I'd go the rest of the way.

I present, the general formula for any N-Minx:

nminx(n) = (((20! / 2) * (3^20 / 3)) * (((30! / 2) * (2^30 / 2)))^(n % 2) * (60! / 2)^(((n + (1 - (n % 2))) - 3) / 2) * (60! / (5!^12))^((((n + (1 - (n % 2))) - 3) / 2) * ((((n + (1 - (n % 2))) - 3) / 2) + (n % 2)))) / (60^(1 - (n % 2)))It is defined as the number of layers to an edge. That is, the Flowerminx / Kilominx is N = 2, the Megaminx is N = 3, the Petaminx is N = 9, etc. It is only valid for N >= 2. The % operator is a modulus so 3 % 2 = 1 and 4 % 2 = 0.

Here are a few interesting values.

Kilominx: nminx(2) = 23563902142421896679424000

Megaminx: nminx(3) = 100669616553523347122516032313645505168688116411019768627200000000000

Master Kilominx: nminx(4) = 9.149 * 10^163

Gigaminx: nminx(5) = 3.647 * 10^263

Teraminx: nminx(7) = 1.151 * 10^573

Petaminx: nminx(9) = 3.164 * 10^996

Examinx: nminx(11) = 7.576 * 10^1533

[...]

Oskarminx: nminx(17) = 4.538 * 10^3829

[...]

Centaminx: nminx(100) = 4.787 * 10^140809