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Overturning Fracsum

Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7

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Building Tetrahedra

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

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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?

Gift of Gems

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Try writing down what each jeweller has after they have all given their gifts.

These four collections all have equal value.

Use this to deduce other statements you can make about the value of each kind of gem.