Over the past few months I've grown to love this community quite a lot. Therefore, I decided to contribute something to you guys. I'm not sure if it's a repost or not, but I wasn't able to find it so far so hopefully it'll prove interesting. The problem is the following:
You are blind. You are also given a deck that consists of 52 playing cards, which naturally have faces and backs. You also like to keep your cards neat and tidy, meaning that all the cards are faced the same way. However, your evil step brother comes in, grabs your deck full of face down cards and takes N cards from it. He then proceeds to turn those N cards face UP and returns them in the deck in that particular way (meaning they are now face up and somewhere random in the deck). However, he also claims that if you manage to separate two packs from the deck, that have an exactly equal number of face up cards he will become your eternal slave until the end of time. Being the genius of your family you are, you win the bet and trick your step brother. How is this possible?
Note 1: The cards are exactly the same, meaning "feeling" which cards are face up is not an acceptable solution.
Note 2: The cards are not bent in any way, meaning that, again, "feeling" which cards are face up is not an acceptable solution.
Note 3: Your step brother tells you exactly how many cards he turned face up in the deck. So, you know the exact value of N.
Note 4: N can practically be any number from 1 to 52.
Emphasis 1: The 2 packs do NOT necessarily need to be equal.
Emphasis 2: When the brother returns the face up cards in the deck, he returns them into random positions, or perhaps shuffles them, it doesn't really matter. What matters is that in the end you end up with 52 cards, N of which are face up.
Well there it is :) This is my first discussion "attempt", so please have pity on me.