Dinner for 15

Fifteen chairs are evenly placed around a circular table on which name cards are placed for fifteen guests. The guests fail to notice these cards until after they have sat down, and it turns out that no one is sitting in front of his own card.
As they want to minimize the number of people who now have to stand up again, they have the idea to rotate the table until at least two of the guests are simultaneously correctly seated.

The question is: Is it guaranteed that there exists a table position where at least two persons are simultaneously correctly seated?

Hint: The key to the problem is the pigeonhole principle.

I want to see the solution.

March 22, 1995
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