Being resilient

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?

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

Can you find an efficent way to mix paints in any ratio?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

What is the same and what is different about these circle questions? What connections can you make?

Explore the relationships between different paper sizes.