13 people came into a hotel with 12 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the thirteenth guest to wait a little with the first guest in room number 1. So in the first room there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, …, and the twelfth guest to room number 11. Then he returned to room number 1 and took the thirteenth guest to room number 12, still vacant.
How can everybody have his own room?
Of course, it is impossible. Into the second room should have gone the 2nd guest, because the 13th guest was waiting in room number 1.