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Upsetting Pitagoras

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

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Lunar Leaper

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

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Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

Overarch 1

Stage: 5 Short Challenge Level: Challenge Level:1

When we have 3 tiles stacked in equilibrium the overall weight of the tiles is (obviously) 3. To balance on the fourth tile the centre of mass of the 3-tile combination must (obviously) be exactly on the edge of the fourth tile.