A Dark Room With Cards

Another week, another riddler. This one is from Blue Taylor:

You’re in a dark room and seated at a table with a deck of 52 cards on it, stacked into a single pile. You also happen to know that currently, within that stack of cards, exactly 13 of them are face up, while all the others are face down.

While you can’t see the cards, you can feel them and move them around. But you can’t tell by touch which cards are face up and which are face down.

How can you make two piles of cards that are guaranteed to have the same number of face-up cards? (And yes, each of these two piles must have at least one card.)

This was a fun problem. The solution:

Create two piles, one with 39 cards and the other with 13 cards. The pile with 39 cards has X that are face up. Therefore the other pile has 13 – X. When you flip every card in that pile over it will have 13 – (13-X), or X cards flipped over — which is the same as the other pile. Easy!

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