OT: I once wondered if normal human shuffling could actually achieve all possible permutations, where by "normal human shuffle" I mean take a deck of cards, split it into two roughly equal piles, and then merge the two piles by repeatedly taking the bottom card from one then the other, with some sloppiness in the "take the bottom card" part so that sometimes you might take more than one card but not too many.
The answer is yes. Here is a way to do it, although it is not very efficient.
Let P be a shuffle where the deck is divided exactly in half, and the merge perfectly alternates one card at a time between piles, starting with the half that was in the bottom before the cut. Let S(n) be a shuffle that is almost a P shuffle except that when the cards that would end up at locations n and n+1 in the P shuffled deck are at the bottom of their piles we drop them in the opposite order then go back to the normal drop order.
S(n) counts as a normal human shuffle. The result of an S(n) shuffle is the same as doing a P shuffle followed by swapping the cards at positions n and n+1 in the P shuffled deck.
If you take any deck and apply the same shuffle repeatedly you eventually get back to where you started. For example doing P 8 times brings you back to where you started. Let O(R) be how many shuffles it takes for shuffle R to come back to where it started, so O(P) = 8.
If you do O(S(n))-1 applications of S(n), then P, then one more S(n), that brings you back to where you started except that the cards at n and n+1 are swapped.
With this we have the capability to exchange adjacent cards in a deck. Any permutation can be reached by a sequence of adjacent exchanges, and thus normal human shuffling can reach every permutation.
As I said this method is not very efficient. The swap of n and n+1 by this method takes 120 shuffles if n is 22 or 28, 72 shuffles if n is 0 or 50, 56 shuffles for 1 or 49, 40 shuffles for 16, 17, 33, or 34, and 16 shuffles for any other n.
Putting the whole deck in a given order would then take tens of thousands of shuffles. Inefficient indeed!
That raises the question of how many normal human shuffles does it actually take to reach a given permutation? What permutation requires the most normal human shuffles?