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Upsetting Pitagoras

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

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?

Seriesly

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

Universal Time, Mass, Length

Age 16 to 18 Short
Challenge Level

When changing units we just need to multiply or divide by a scaling factor. You can use common sense to decide whether to multiply or divide.