If you didn’t focus on mathematics today, you should at least keep the gears in motion by trying to solve this mathematical puzzle.

You are blindfolded, then given a deck of cards in which 23 of the cards have been flipped up, then inserted into the deck randomly (you know this). Without taking the blindfold off, rearrange the deck into two stacks such that both stacks have the same number of up-flipped cards. (You are allowed to flip as many cards as you please).

What’s your solution?

mendelHow many cards are in a full deck? 52? Or doesn’t it matter?

VDoesn’t matter. See my solution below, and replace 29 with the number of your choice.

VSimple.

Split it into two stacks for size 23 and 29 each. Lets say x flipped cards are in the first stack. Second stack contains 23-x flipped cards.

Flip all the cards in the 23 stack. Now it contains 23 – (23-x) = x flipped cards.

KirkV, your English is not that good.

Here is how it should be.

Divide the deck into two decks of size 23 and x-23 where x is the total number of cards.

Flip the deck with 23 cards.

Done.

Solution:

Let y be the number of flipped cards in the deck with 23 cards.

Deck with 23 cards will have y flipped cards.

Deck with x-23 cards will have 23-y cards.

After you flip the deck with 23 cards, the number of flipped cards in it will be 23-y which is equal to the number of flipped cards in the other deck.

Done.