Unequal Halves
You are blindfolded, then given a deck of 52 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.)
If number of cards in the 2 stacks are a and b, such that a>b, then type b as the answer.
The answer is 23.
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1 solution
If we make the stacks consist of 23 and 29 cards each:
Let x=number of cards flipped up in the stack of 23 cards. Then there are 23-x flipped-up cards in the other stack.
Then flip all the cards in the stack of 23 cards. So now there will be 23-x flipped-up cards in the stack of 23 cards, which is the same as the number of flipped-up cards in the other stack.
Hence b=23