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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?


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?


Age 14 to 16
Challenge Level

Find the exact values of $x$, $y$ and $a$ satisfying the following system of equations:
\frac{1}{a+1}&=a-1 \\
x+y&=2a \\