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In Particular

Write 100 as the sum of two positive integers, one divisible by 7 and the other divisible by 11. Then find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers.

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Garfield's Proof

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

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For What?

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

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Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
This problem gives opportunities to address processes that need splitting into parts.

The path of the light ray switches direction at intervals, and handling that is crucial to the problem.