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Answer: 8

If the squares are numbered 1 to 6, as shown.

 
   1  
 		  
   3  
 		  
   5  
 
 
   2
 		    4    6


The possible pairings are:
1 and 4 
1 and 5
1 and 6
2 and 3
2 and 5
2 and 6
3 and 6
4 and 5

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.