Solution to: Cards with Crosses
Take 14 cards from the stack. Of these 14 cards, k cards are with the cross up and therefore 14-k cards are with the circle up. In the remaining stack of 9 cards are 14-k cards with a cross up.
Then turn the stack of 14 cards round. Now there are 14-k cards with a cross up in both stacks.
Note that we do not know exactly how many cards are lying with a cross up in both stacks (or how many cards are lying with a circle up). We only know that both stacks have the same number of cards with a cross up.