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.)
soln | Comment 1 of 3
I think there is only one total possible no matter how you fill:
(n-1) n^2 

I look at it this way: The order in which the cells of a row are filled is immaterial. Always you will gain 0, 1, 2, ..., n-1 game points with each successive fill-in (not necessarily made on successive turns), counting the growing number of elements in that row.  So, by the end, each row contributes sum(n-1) = (n-1) n/2. Row and column contributions build independently but increase in the same way. Since there are 2n rows and columns: Total = (2n) (n-1) n/2 = (n-1) n^2

Edited on December 7, 2020, 9:46 am
  Posted by Steven Lord on 2020-12-07 09:07:19

Please log in:
Remember me:
Sign up! | Forgot password

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

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