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Choose any three by three square of dates on a calendar page...

Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Tri-colour

Age 11 to 14 Challenge Level:

If each point is joined to every other point then this makes (6 x 5)/2 = 15 line segments. All the line segments are coloured either red or green.

Joel of ACS (Barker), Singapore proved that there must then be a triangle all of whose sides are the same colour. This is his solution:

Label the points from A to F. Out of the line segments connected to A, at least 3 have to be the same colour, (let's say AB, AC and AD are red). Then BC has to be green, because otherwise ABC will be all red. Ditto for CD and BD. So BCD will be all green.