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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...

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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.

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Peeling the Apple or the Cone That Lost Its Head

How much peel does an apple have?

Under the Ribbon

Stage: 4 Challenge Level: Challenge Level:1

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 ?