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Building Tetrahedra

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

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?

Polycircles

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Fruity Totals

Age 7 to 16
Challenge Level

Which row/s and/or column/s give you useful information?
Can you combine or compare rows and/or columns?
Which fruit is the easiest to work out the value of first?