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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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Square Mean

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

Loopy

Age 14 to 16 Challenge Level:
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.
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