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 .