### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

# Named Products

##### Stage: 4 Short Challenge Level:

If we rewrite the equation we get the product $E\times I\times G \times H\times T = T\times W \times O\times F\times O \times U \times R$.

There are $10$ different letters here, so each number from $0$ to $9$ must be represented by one of the letters. So one letter is $0$. Any product where this letter appears is $0$. Hence both sides must include this letter. The only letter on both sides is $T$.

Hence $T=0$ and the product $T\times H\times R \times E \times E =0$.

This problem is taken from the UKMT Mathematical Challenges.