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Let \(p(n)\) denote the number of people in the correct seat when the table is rotated by \(n\) people. From the question, we know that:

As every guest can be put into the correct place by one rotation, we know that:

As \(p(0)=0\):

This sum has 23 positive integers adding up to 24, so one of the rotations must lead to at least two people being in the correct places.

Extension

If the 24 guests sat randomly and one person was in the correct seat, could you still rotate the table so that two people are correctly seated?

$$p(0)=0$$$$p(0)+p(1)+...+p(23)=24$$$$p(1)+...+p(23)=24$$