This note has been used to help create the Combinatorial Games - Winning Positions wiki
Since everyone is posting challenges lately, might as well post one that I've heard:
You, your friend, and the Devil play a game. You and the Devil are in the room with a \(8 x 8\) chess board with \(64\) tokens on it, one on each square. Meanwhile, your friend is outside of the room. The token can either be on an up position or a down position, and the difference in position is distinguishable to the eye. The Devil mixes up the positions (up or down) of the tokens on the board and chooses one of the \(64\) squares and calls it the magic square. Next, you may choose one token on a square and flip its position. Then, your friend comes in and must guess what the magic square was by looking on the squares on the board. Show that there is a winning strategy such that your friend can always know what square the magic square is.
You MAY flip a token. As in, you are not forced to flip a token; you may choose to not flip a token.
You can't just tell your friend what square it is. Or point to it. Or text him it. Or... you get the point.
Your friend knows the strategy as well (you tell him beforehand).
If you don't get it right, the Devil takes your soul. High stakes.
There are many ways to approach this problem. Some are more reproducible (i.e. real humans could more reasonable do it) than others. There do exist solutions that humans can reproduce.