Can you make a tetrahedron whose faces all have the same perimeter?
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?
Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?
Clearly if $a$, $b$ and $c$ are the lengths of the sides of a
triangle and the triangle is equilateral then
$a^2 + b^2 + c^2 = ab + bc +
Is the converse true, and if so can you prove it? That is if
$a^2 + b^2 + c^2 = ab + bc + ca$ is the triangle with side lengths
$a$, $b$ and $c$ necessarily equilateral?