Here is a half of a magic trick to impress your friends. Take the Ace to Seven of hearts and order them numerically in a pile with Ace at the bottom and Seven at the top. Do the same with the Ace to Seven of spades. Put the pile of spades on top of the pile of hearts. Flip the
Make a cut anywhere. Deal out
Your friend chooses two nonnegative numbers that add up to
Your friend now chooses two nonnegative numbers that add up to five and repeat the same procedure. We will continue doing this, but at each turn, the total number of swaps decreases by one. Eventually, we should have one card remaining in each pile. It turns out to be a matching pair.
How does the trick work?