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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
At what distance down the corridor will the ray of light pass through the centre line again?

At what distance down the corridor will the ray of light pass through the centre line again going in the same direction as it was initially?