Before doing this problem, it would be a good idea to look at Ring a Ring of Numbers
Change the ring so that there are only 3 squares.
Can you place three different numbers in them so that their differences are odd?
Can you make the differences even?
What do you notice about the sum of each pair in each case?
Try with different numbers of squares around the ring.
What happens with 5 squares? 6 squares?
What do you notice?
Full size version
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.
This problem is based on an idea taken from "Apex Maths Pupils' Book 2" by Ann Montague-Smith and Paul Harrison, published in 2003 by Cambridge University Press.