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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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Seriesly

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

Before attempting this problem is it interesting to ask students to make a scale sketch of their best intuitive guess at the answer.

Once the answer is found the students can compare their intuition with reality. Were they roughly correct? Does their answer give them any clues as to the form of a larger compound structure?

Ask students to explain in words why their structures only just balance, as producing a clear verbal explanation will reinforce the understanding of the underlying mechanical principles.