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Can you make a tetrahedron whose faces all have the same perimeter?

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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.