You may also like

problem icon

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.

problem icon

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.]

problem icon

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?

Age 14 to 16 Challenge Level:
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?