Take all the face cards out of a deck of playing cards. Keep all the numbered cards, counting ace as 1, and hand them to a friend. Your friend takes one card out of the deck and gives you back the rest. How can you tell which numbered card is gone?

## Solution

There should be four 1's, four 2's, and so on up to four 10's. This totals 4x(1+2+3+...+10) = 4x(10x11/2) = 4x55=220. Add up the cards that you have, and you will be a bit short of that 220. If your sum is 216 the missing card is a 4. To find the suit of the 4 just scan through the deck quickly and you can see which 4 isn't there.