KöMaL problem A, 2021

Combinatorics Difficulty 6.0 National Olympiad Prove it Hungary

The following game is played with a group of $n$ people: $n+1$ hats are numbered from $1$ to $n+1$ . The people are blindfolded, and each of them is getting one of the $n+1$ hats on his head (the remaining hat is hidden). Now a line is formed from the $n$ people, and their eyes are uncovered: each of them can see the numbers on the hats of the people standing in front of him. Now starting from the last person (who can see all the other players) the players take turns to guess the number of the hat on their head, but no two players can guess the same number (each player hears all the guesses from the other players).

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