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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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Bang's Theorem

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

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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:1
In this problem you are only given enough information to find the values of rubies, saphires and diamonds relative to the price of a pearl.

Try writing down what each jeweller has after he has made his gift. These four collections all have equal value. Use that to find other statements you can make about a number of one kind of gem matching for value a number of another kind of gem.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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