### Bang's Theorem

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

### 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?

# Kangaroo Subtraction

##### Stage: 3 and 4 Short Challenge Level:

In the subtraction calculation below, each of the letters K, A, N, G, R and O represents a different digit.

$\ \$ K A N
- G A R
$\ \ \ \ \$ O O

What is the largest possible value of the number 'KAN'?

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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