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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?

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Medallions

Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?

Loopy

Stage: 4 Challenge Level: Challenge Level:1
The terms $a_1, a_2, a_3,...\ a_n,...\ $ of a sequence are given by: $$a_n =\frac{1+a_{n-1}}{a_{n-2}}.$$ Investigate the sequences you get when you choose your own first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture? Investigate the sequences.
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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NRICH is part of the family of activities in the Millennium Mathematics Project.