### 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 Â£20 to see an exhibition. The admission price is Â£3 for men, Â£2 for women and 50p for children. How many men, women and children are there in the group?

### Our Ages

I am exactly n times my daughter's age. In m years I shall be ... How old am I?

# Deep Roots

##### Age 14 to 16Challenge Level

Find integer solutions to: $${{\sqrt{a + b\sqrt{x}}} + {\sqrt{c + d\sqrt{x}}}} ={ 1}$$

Hint: As everything on the left is positive and the total is 1, there are only a few cases to consider.