This is an old but good puzzle, which I personally enjoyed solving quite a while ago.
Seats of the round table are all labeled with the names of N managers. All managers have chosen the wrong seat. Prove that you can always rotate the table so that at least two managers sit in the positions with the correct names.
This problem is quite simple, so I don’t provide the solution, but feel free to share it in comments. As a hint, I can say that the whole solution shouldn’t be longer that one or two sentences.