Given a 3x3 tic-tac-toe grid.
If you are allowed to place just one X in each of the small squares, what is the greatest number of Xs that can be put without getting "three in a row" in any of the 8 directions?

How many distinct solutions are there?

Since the most each row and column can hold without yielding "three in a row" is two in each and there are three rows and three columns (each with two in them) then there cannot be more than six X's in the solution (the two that fill each row will also fill the columns).

The solution looks like this:

  X |  X |    
---+---+--- 
  X |     | X 
---+---+---
     |  X | X

The only other solution to this is a rotation of this same solution, so there is only one six X solution.

Posted by Astilius on 2014-12-12 09:18:47