Ring a Ring of Numbers

'Ring a Ring of Numbers' printed from https://nrich.maths.org/

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Ring a Ring of Numbers printable sheet

Here is a picture of four numbers placed in squares on a circle so that each number is joined to two others:

Four numbers positioned on a circle as if they were at the 12 o'clock, 3 o'clock, 6 o'clock and 9 o'clock positions of a clock face. Reading around in a clockwise direction from the 12 o'clock position, the numbers are: 2, 4, 9, 1

What do you see?
What do you notice?

Choose four numbers out of 1, 2, 3, 4, 5, 6, 7, 8 and 9 to put in the squares so that the difference between joined squares is odd.
Only one number is allowed in each square. You must use four different numbers.
What can you say about the sum of each pair of joined squares?

What must you do to make the difference even?
What do you notice about the sum of the pairs now?

Here are some sheets for recording your solutions.

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.