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Plum Tree

Label this plum tree graph to make it totally magic!

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Magic W

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Chocolate 2010

Age 14 to 16 Challenge Level:

This looks like a fairly standard problem leading to a simple algebraic equation that can be solved, however the need to examine what is happening to each of the digits of the number means that the solution requires a little more thought and an appreciation of place value.

Being able to generalise this to any year may help convince you that the structure of the problem is understood.