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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?

Janine's Conjecture

Age 14 to 16 Challenge Level:

Janine noticed, while studying some cube numbers, that ``if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number cubed''; e.g., 3, 4, 5 gives 3 x 4 x 5 + 4 = 64, which is a perfect cube. Does this always work? Can you prove or disprove this conjecture?