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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?

Balance Point

Age 14 to 16 Challenge Level:

Students need to be familiar with the principle of moments.
The problem called "Inside Outside" will help with this.

This problem requires careful systematic working and the utilisation of symmetry to reduce the arrangements to be tested to a manageable number (12).