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Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Tree Tops

Can you make sense of information about trees in order to maximise the profits of a forestry company?

Under the Ribbon

Age 14 to 16
Challenge Level

A ribbon is nailed down with a small amount of slack.
The distance between the nailed ends is 1 metre and the amount of ribbon is 104 cm.

What is the largest cube that can pass under the ribbon ?

And where along the ribbon is the best place for the cube to pass under, or doesn't the position matter ?


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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