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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.

Training Schedule

Stage: 4 Challenge Level: Challenge Level:1

Joseph from Park View Community School sent us the following solution:
Find the percentage away from the world record for each event. Increase the 3 lowest events by 20% and accordingly maintain current levels for the 3 greatest events. increase performance by 10% on the remaining event. I calculated all points including all percentage increases as well using excel.

You can download Joseph's spreadsheet to see how he calculated this solution here.