# Card Trick Riddle

I ask Alex to pick any 5 cards out of a deck with no Jokers.

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Peter can’t see any of this). I look at the cards and I pick 1 card out and give it back to Alex. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Peter.

Peter looks at the 4 cards i gave him, and says out loud which card Alex is holding (suit and number). How?

The solution uses pure logic, not sleight of hand. All Peter needs to know is the order of the cards and what is on their face, nothing more.

When the 5 cards are picked at random, this is only possible when the “neat” pile isn’t that neat.

The suit is easy. With five cards there is at least one suit with 2 or more cards. Pick one of those cards and put the other one at the top. The value can be coded in binary, horizontal means 0 and vertical means 1. With 4 cards you can code up to the number 15. So the pile passed to Peter will contain cards arranged both horizontally and vertically.

When all the cards needs to be arranged vertically (or horizontally) there is no easy solution possible (if there is any solution at all). When you use 1 card for the suit, you only have 3 cards to indicate the value. In the worst case those 3 cards could have the same value (e.g. 3 aces) and there are only 6 ways to order those 3 cards. And there are 12 possible values of the card Alex has.

### Your Answer

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