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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?

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I keep three circular medallions in a rectangular box in which they just fit with each one touching the other two. The smallest one has radius 4 cm and touches one side of the box, the middle sized one has radius 9 cm and touches two sides of the box and the largest one touches three sides of the box. What is the radius of the largest one?


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

At a well known store they sell their own blend of coffee. They use:

Mocha costing £13 per kilogram
Kenyan costing £14 per kilogram
Brazilian costing £17 per kilogram

To make 11 kilograms of this blend of coffee costs £15 per kilogram.
This blend uses more Brazilian than Kenyan coffee.
An exact number of kilograms of each type of coffee is used.
How many kilograms of each type of coffee are used?