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A Puzzle In Paradox

published on November 1st, 2007 . by Vanaja
Thirteen teachers are in Paradox, a math conference. When they arrive at the Enigma Hotel to check in, they are told that only 12 rooms are available. Since their school had made reservations for 13 rooms, the teachers are a bit upset that they will have to find another place to stay. As they are preparing to leave and find another hotel, the manager comes out and asks if there is a problem. When she hears of their situation she assures them that the Enigma Hotel has enough space to accommodate each teacher in his or her own room. She takes two of the teachers to room #1 and promises to come back in a few minutes and take one of them to another room. She takes the third teacher to room #2, the fourth teacher to room #3, the fifth teacher to room #4 and so on, taking the twelfth teacher to room #11. She then returns to room #1 and escorts the extra teacher waiting there to room #12. All of the teachers are now happily settled in their own rooms.

Is this possible? Why or why not? question

O.K Here is the solution.

Actually, it is not possible. When the manager is putting the 12 th teacher in #11, the 13 th teacher is still waiting there and he or she must go to the #12 room. So, all the rooms are now occupied and in the first room there are two teachers and the teacher waiting there can not go to the #13 room.