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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?

Power Quady

Stage: 4 Challenge Level: Challenge Level:1

Why do this problem?
This is a short problem that can be used as a lesson starter and it is non-standard so the learners have to think how to apply what they know. The problem also requires the learner to work systematically to be sure they have considered all possible cases and found all the solutions.

Possible approach
Let the class work on the problem and then make a list of all the solutions that they have found.

Key Questions
Have we found all possible solutions?
How can we be sure?