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Tic tac toe points (Posted on 2020-12-07) Difficulty: 3 of 5
You have an n × n grid of empty squares. You place a cross in all the squares, one at a time. When you place a cross in an empty square, you receive i+j points if there were i crosses in the same row and j crosses in the same column before you placed the new cross. Which are the possible total scores you can get?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution Solution (spoiler) | Comment 2 of 3 |
I agree completely with Steven Lord.

To put it a little differently, all we are counting is the total number of "handshakes", if every cell shakes hands with every other cell in their row and column.  There are n^2 cells, and and each shakes hands with 2(n-1) other cells, but we need to divide by 2 to avoid double-counting.  So, n^2 * 2(n-1) / 2 = (n-1)n^2

  Posted by Steve Herman on 2020-12-07 18:01:46
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