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Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

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Two Cubes

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

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Square Mean

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

How Old Am I?

Stage: 4 Challenge Level: Challenge Level:1
If I am $x$ years old now how old was I 15 years ago?
If I am $x$ years old now how old will I be in 15 years' time?
Can you use these expressions to form an equation to solve?