Number Differences

Number Differences


You might like to try A Ring of Numbers and More Rings of Numbers before this problem.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. (You must use each of the numbers once.)
Can you find some other ways to do this?
Is it possible to put the numbers in the squares so that the difference between joined squares is even?
Explain your answer.
What would you need to change for it to be possible?
What general statements can you make about odd and even numbers?

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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. To order a copy of this book, or others published by CUP, see their online catalogue .

 

Building on Ring a Ring of Numbers and More Numbers in the Ring , this problem encourages pupils to form early stages of proof by using their knowledge of odd and even numbers to construct mathematical arguments, leading to generalisation. If not using the interactivity, it may be useful for children to have a sheet of blank grids in order to try out their ideas.