More Numbers in the Ring

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

More Numbers in the Ring printable sheet

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More Numbers in the Ring
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 three 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?

 

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.