Hint to Puzzle #36: N Face Up Cards In A Dark Room

36. You are in a dark room with a deck of cards. N of the cards are face up and the rest are face down. You can't see the cards. How do you divide the deck in to two piles with equal numbers of face up cards in each?

Let's look at some things the puzzle does and doesn't say.
  • It doesn't say we need to create two equal piles of 26 cards. It just says two piles with the same number of face up cards, nothing about the number of face down cards.
  • It doesn't say that they need to be the same cards that are face up as at the start of the puzzle or that the same number of cards should be face up.
  • It is assumed that we know the value of N.
Here is a deck for you to consider. Blue is face down, red is face up and N=10, there are 10 face up cards.

1 pile of cards N are face up.

The answer is astonishingly simple, and as always contains no slight of hand, no tricks.

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