Creating and manipulating expressions and formulae

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

What is special about the difference between squares of numbers adjacent to multiples of three?

If you know the perimeter of a right angled triangle, what can you say about the area?

Can you explain what is going on in these puzzling number tricks?

There are unexpected discoveries to be made about square numbers...

A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

If a sum invested gains 10% each year how long before it has doubled its value?

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.