In the grids shown and mentioned below you must select 2 squares in the 2X2 grid, 3 squares in the 3X3 grid etc.

Rules
You must select the squares so that no two squares are in the same row or column. Find as many ways as possible to do this for each grid.

e.g. 

• How many solutions are there for a 2X2 grid? 
  How do you know you have found them all?
• How many solutions are there for the 3X3 grid?
  How do you know you have found them all?
• Describe any patterns you see in the way the solutions look. 
  How can these patterns help you determine if you have found them all?
• Describe three different ways you could organise your solutions based on the patterns you discovered. 
  Use these grids below to show one of these ways.
  
  
  
  
• How many solutions do you think there would be for a 4X4 grid and why?
• What about a 10X10 grid?
• Can you write a statement to tell how many solutions for any number of squares?
  
  

  Number of Squares	Number of Ways
  2
  3
  4
  10
  100
  n

  
  Answer

This investigation came from The Maths' Connection published by Family Maths Trust