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Placing Chess With Some Forbidden Restrictionscheckers with some restrictions

There is a (n x n) chessboard.

We are going to put n chess checkers on itan (n x n) checkers board, with the following restrictions:

1) In each column there is EXACTLY one chesschecker.

2) For i=1,2,...,(n-1), the first i rows cannot have EXACTLY i chesscheckers.

The question is to count the number of ways to do so. I guess that the answer is n^{n-1} (while if restriction 2) is removed, the answer is obviously n^n)n^{n-1}, but I do not know how to prove it. Can anyone help?

(If restriction 2) is removed, the answer is obviously n^n.)
show/hide this revision's text 1

Placing Chess With Some Forbidden Restrictions

There is a (n x n) chessboard. We are going to put n chess on it, with the following restrictions:

1) In each column there is EXACTLY one chess.

2) For i=1,2,...,(n-1), the first i rows cannot have EXACTLY i chess.

The question is to count the number of ways to do so. I guess that the answer is n^{n-1} (while if restriction 2) is removed, the answer is obviously n^n), but I do not know how to prove it. Can anyone help?