Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.

On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?

If you want to understand mathematically, let us say that there were x inverted cards in the top 15 cards of the deck. Then the remaining 37 cards will comprise of 15-x number of inverted cards.

If we reverse the 15 cards the number of inverted cards will become 15-x and the number of inverted cards will be same in both the piles.