- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

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.

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.]

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

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?

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?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.

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NRICH is part of the family of activities in the Millennium Mathematics Project.

NRICH is part of the family of activities in the Millennium Mathematics Project.