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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:

Start with a diagram of a cube just passing under a ribbon.

And maybe put the cube exactly in the middle, just to start with.

Next choose a size for the cube, any size, and calculate how long the ribbon would be if that was the biggest cube that would fit.

Was it 104 cm ? Adjust the cube size and try again ?