SOLUTION: A clerk had only 10 vacant rooms left in one hotel. There were 11 men who went into the hotel at the same time, each wanting a separate room. The clerk, settling the argument said,

Algebra ->  Permutations -> SOLUTION: A clerk had only 10 vacant rooms left in one hotel. There were 11 men who went into the hotel at the same time, each wanting a separate room. The clerk, settling the argument said,      Log On


   

Question 600069: A clerk had only 10 vacant rooms left in one hotel. There were 11 men who went into the hotel at the same time, each wanting a separate room. The clerk, settling the argument said, "I'll tell you what I'll do. I will put two men in Room 1 with the understanding that I will come back and get one of them a few minutes later." The men agreed to this. The clerk continued, "I will put the rest of you men as follows:
the 3rd man in Room 2
the 4th man in Room 3
the 5th man in Room 4
the 6th man in Room 5
the 7th man in Room 6
the 8th man in Room 7
the 9th man in Room 8 and
the 10th man in Room 9
Then the clerk went back to get the extra man he had left in Room 1, and put him in Room 10. Everybody is happy. What is the fallacy of this plan?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st and 2nd man are placed in Room 1. When the clerk comes back to Room 1, either the 1st or 2nd man gets placed in Room 10. That still leaves the 11th man without a room.