All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information