Comment by EmilyHughes

Whats so crazy about it though? Intuitively it seems very likely to me that all possible states of 2028 would fit into a 64 bit number.

4x4 = 16 tiles, 64/16 = 4 bits, 16 powers of two = space for 0-65536 per tile.

So going up to only 2048 would leave some room even.