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?

Polycircles

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Matchless

Age 14 to 16Challenge Level

There is a particular value of $x$, and a value of $y$ to go with it, which make all five expressions equal in value.
Can you find that $x$, $y$ pair?

Did you have more information than you needed to solve the problem?