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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.

Triangular Triples

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.


Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Triangles Within Squares

Age 14 to 16
Challenge Level
Why not encourage pupils to discover rules of their own?

This problem links to "Triangles withinTriangles " and the problem "Triangles within Pentagons"

There are many different ways to visualise this question and pupils should be encouraged to explain how they "know" their rule works.