[yafmsrnp] 6144

Take 4 squares of the same size. There are 6144=4!*4⁴ ways of fitting those squares into a 2x2 block, counting rotations. A surprisingly large number for such a simple problem. Perhaps it can be the basis for a PIN or combination lock.

Surprisingly if you quarter a 3x3 or 3x4 array into 4 rectangular blocks at a lattice point, you get the same number again 6144 (counting each possible internal lattice point) though you lose uniqueness among the final permutations. Swap a 1x3 and 2x3, each of those can be cut two different ways.