Riddles with a mathematical twist I am looking for riddles that are understandable for everyone(so especially non-mathematicians) but require mathematical knowledge or deep abstract ideas to be solved.
The best answer will be the riddle that is most understandable( especially not contain any abstract math at all, so for example fermat's last theorem is NOT what I am looking for) but most mathematically demanding at the same time.
(I hope it is clear how I will try to objectively assess the answers, so that no one has to vote for closing this thread)
Also it would be nice, if the riddle you recommend is not very famous.
 A: Although not needing deep mathematical knowledge...


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*A blindfolded man is handed a deck of 52 cards and told that exactly 10 of these 
cards are facing up. How can he divide the cards into two piles (possibly of different 
sizes) with each pile having the same number of cards facing up?


An old-fashioned implication one:


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*Mrs Claus always sneezes just before it starts snowing. She just sneezed. 
“This means that it’s going to start snowing”, thinks Santa. Is he correct? 


Robbed these from http://math.alamzy.com/wp-content/uploads/2012/10/Handbook.pdf
A: Puzzles based on Ramsay Theory could qualify. For example, there are 9 people in a room for a meeting. Amongst any three there is at least one pair who have never met before. Show that there is a group of four people amongst the nine who were mutual strangers before the meeting.
A: Hilbert's hotel questions could be what you are looking for:
suppose that Hilbert has a hotel which has inifinitely many rooms. The only rule is only one person can accomadate in a room. A bus comes with infinitely many seats to the hotel. etc. 
A: The four color theorem is easy to explain but hard to prove. However, it's quite famous. 
As a variation, you could ask how the following picture can be repainted with only four colors.

(Source: Wikipedia)
A: A small company (say $N$ people) are going to have a team-building exercise. The exercise manager tells the group to stand in a line, and explains that he will hang a red or a green water balloon above the head of each one. Everyone will be able to see the balloons in front of him/her, but cannot see his/her own or the ones behind.
The exercise manager will ask each person in order, from the back, what colour the balloon above his/her head is. If the answer is wrong, the balloon is popped, otherwise it is not popped.
The group are to discuss beforehand for a few minutes to come up with a strategy for what colour each one should say, but once they are in the line no more communication is allowed.
If they want to minimise the number who get wet, what strategy should they employ? What is the smallest number of popped balloons that they can guarantee?
(Source: I'm not sure, but I believe it was in the Swedish onboard train magazine Kupé.)
A: I wonder why treasure problem in One Two Three Infinity is not mentioned yet. It doesn't require very deep maths. Yet, still asks for some mathematical tools. 
Problem (took liberty to change language a bit):

There was a young and adventurous man who found among his great-grandfather's papers a piece of paper that revealed the location of a hidden treasure. The instructions read:
"Sail to ___ North latitude and ____ West longitude where you will find a deserted island. There lies a large meadow on the north shore of the island where a lonely oak and a lonely pine stands. There you will also see an old gallows on which we once hang traitors. You start walking from the gallows and walk to the oak counting your steps.
  At the oak, you must turn right by a right angle (90degree) and take the same number of steps. Put here a spike in the ground. Now you must return to the gallows and walk to the pine counting your steps. At the pine you must turn left by a right angle and see that you takes the same number of steps, and put another spike into the ground. Dig halfway between the spikes; the treasure is there."
The instructions were quite clear and explicit, so our young man chartered a ship and sailed to the South Seas. He found the island, the field, the oak and the pine, but to his great sorrow the gallows was gone. Too long a time had passed since the document had been written; rain and sun and wind had disintegrated the wood and returned it to the soil, leaving no trace even of the place where it once had stood.

The question is "How to find the treasure?"
Pros:
 There are multiple ways to solution


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*An elegant one using geometric interpretation of $i$ as is done in the book

*Using high school trigonometry

*Using vector algebra (very similar to the last one)

