A 3x3 Rubik's cube provides a way of encoding 65 bits, though the problem of mapping cube states to numbers, especially of mapping them one-to-one, is left unsolved. Like shuffling a deck of cards, it provides a convenient way of generating 65 bits of entropy, assuming hand scrambles can be trusted.

It is not too suspicious to be found carrying a scrambled Rubik's cube. Carrying two identically scrambled Rubik's cube (a backup key) might be suspicious, but the nature of the backup could be concealed by (say) applying an easily reversed checkerboard algorithm to it. (Creating two identically scrambled cubes is analogous to solving a cube.) Store the cubes in boxes so they do not get accidentally turned.

A supercube (picture cube) provides exactly 11 bits more, or 76 bits.

4x4 cube 152 bits. 5x5 cube 247 bits. 6x6 cube 385 bits (but almost 386).

Megaminx 225 bits. Gigaminx 875 bits. Teraminx 1903 bits. Petaminx 3310 bits.

Previously, code for computing the number of combinations.

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