### Building Tetrahedra

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

### Rudolff's Problem

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

### Medallions

Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?

# Square LCM

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

The highest common factor of two positive integers $m$ and $n$ is $12$, and their lowest common multiple is a square number.

How many of the five numbers $\frac{n}{3}$, $\frac{m}{3}$, $\frac{n}{4}$, $\frac{m}{4}$ and $mn$ are square numbers?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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