XOR and Factorial
How could XOR be related to a factorial? If you remember my yearly posts, they were about Sierpinsky's triangle, which is itself constructed using either xor or factorial, so no magic in there.
Anyway, why would one need to shuffle stuff quickly?
1. Encryption: if you use user password to permutate alphabet letters, you get result equivalent to XOR-cypher, like the one used to encrypt Might & Magic 4 files (yay! another XOR-factorial connection!!!).
2. Raytracing: given sufficiently complex scene for additional difficulty placed in a non-euclidean space (say a fractal), we can't just shot rays linearly to probe the space, and there are rather large number of possible rays, we can permute than number and pick and random set of rays, which should eliminate bias (yeah, like in that Sussman & Minsky joke).
3. Roguelikes: say you have a set of 10 premade rooms and 10 slots in a dungeon, now we need to somehow map these 10 rooms to 10 slots, which will result in 10! possible dungeon variations.
4. Card games obviously, where you need to place all cards in a random sequence.