### 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.

# Fibonacci Deduction

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

If we let the fifth number be $x$, then the sixth number is $6+x= 15$, so $x=9$.

The seventh number is the sum of the fifth and sixth numbers, $9+15=24$.

This problem is taken from the UKMT Mathematical Challenges.