140/3 or 46 2/3 pies
edit: is my math right? someone confirm.
edit #2: my math is right -- 7 x 6 (2/3) = 46 (2/3), riciardos had me worried
Here is my favorite riddle of all time. It is both long and hard. (After much thought, I managed to get it mostly right and was immensely proud of myself).
If you have heard this riddle, please don't answer it, because this riddle is a beautiful thing (i think)
here goes:
23 young prisoners are summoned together by the warden of their jail. They are all in solitary confinement for life, no possibility of parole. The warden tells them that he has an idea for a game. And maybe they could win their freedom. The game is as follows:
The prisoners will all be split up after this meeting, never to see eachother or contact each other again. Solitary confinement. At random, and at the warden's whim, a single prisoner will be taken out of his cell and secretly brought to a room. The only thing in this room is two switches. Each of these switches has two positions -- up and down. The prisoners do not know who amongst them will be brought in first or the initial position of the switches.
Every time a prisoner is brought into this room, he MUST flick one and ONLY one of these switches. He cannot leave the switches as they are. He cannot touch anything else in the room or leave any kind of marking, scent, or disturbance of any sort (besides flicking the switch) under pain of death. Once he has flicked a switch, he will be escorted back to his cell, carefully watched so that he disturbs nothing. The room will be sealed and not disturbed at all until the next prisoner is brought in to find it exactly as the last one left it.
The warden will continue randomly selecting prisoners to bring to the switch room indefinitely. There may be long waits (days, weeks, months) in between the warden's summonings, and some prisoners may wind up going many times before others go once, but eventually every single prisoner will go to the room and continue going until the game is stopped.
The game is stopped when any prisoner summons the warden and tells him that every prisoner (all 23) has been in the switch room at least once. If that prisoner is right, all 23 of the men are released from prison. If that prisoner is incorrect, all 23 are immediately rounded up and executed. Once again, during this game, there will be no communication of any sort in between the prisoners.
So, after the warden presents his game, the men gather round and are allowed to talk to eachother for the last time. They all agree that they want to play the game (since they're all young men with long sentences) and they also all agree that no one is willing to risk death by guessing that all the prisoners have gone to the room. No one will summon the warden until he is absolutely positive that everyone has been in the room. They mulled it over, trying to find a solution. After a bit, a clever prisoner came up with an idea that was accepted. They played the game and found themselves free men.
What was this clever plan?
If you answer this question (or even get really close), feel very smart and good about yourself. However, resist the urge to prove how smart you are to everyone else, and post the answer in black, please.
Hint:
There are no tricks here -- this prisoner found a true solution.
I may add other hints if people need em.
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