For a very long time I looked for hard puzzles on the internet. The kind of puzzles I like is actually very difficult to find. I'll explain it : I like puzzles that can be easily explained, that seems impossible to solve a priori and whose answers make you think intelligence or logic is awesome. I'll give you examples of the only four enigmas I know and that satisfy those criterias (each one can be found on this forum ) :

1.

10 peoples are placed in independant boxes at t=0. After a random time interval, a machine take a random people and put him in a room where there is just a switch (nothing else). Then, after a random time interval it put the people back in his box. At the begining the switch is off.

These people must ellaborate a strategy, before beeing put in the boxes, so that it is possible for one of them to say, at any given moment, "now I know that the nine others have been put in the room". Is it possible ?

2.

A monastery is full of monks who have made a vow of silence (there is more than one monk). One day some monks become ill. The only symptom is a blue spot in the forehead so that a monk doesn't know when he is ill but he can see the other ones who are. When a monk know he is ill, he will immediately left the monastery and go to the hospital. The monks can see everyone else once a day during great dinner.

After a year have passed, every sick monk go to the hospital, without having broken their vow of silence. How many monks where ill at the beginning?

3.

100 mathematicians are beeing emprisonned by an evil dictator. One day he imagines a silly game : he puts the mathematicians in a row so that the last one can see the 99 ones that are in front of him, etc. He puts a colored hat on the head of each mathematician. There are three colors : red, yellow and green. And then he says : each one of you, starting from the last one (the one who can see each other) will try to guess the color of his hat. If his guess is right he will be freed if he is wrong he will be executed."

What strategy the mathematicians should choose to save most of them ?

4. (this one requires real bases of mathematics but I still found the result amazing)

500 students are gathered in a room. Their headteacher start speaking : "On the following room there are 500 numbered lockers. Each locker contains the name of a student. After your name is called you will go in this room, and you will open 250 lockers. If anyone of you can’t find his name among those lockers the game stops. You will go back into your room and we will start again tomorrow after I rearranged the names in the lockers randomly. You will be able to go on vacation only when everyone has found his name."

Can the students adopt a method that would probably assure them to be on vacation in a week ?

This topic is adressed to people who already know those puzzles and who can give me links to similar ones. It is not a topic for answering the puzzles I gave.

PS : I read the puzzle about the mathematicians in a circular prison :

http://forums.xkcd.com/viewtopic.php?f=3&t=70558&sid=c7ad9cc397f88009a8dbb4c3cbcb3e08

but, though it is a really nice puzzle, i found the answer way much complex to be explained orally.