1230.65 – Identify the card

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?


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.