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?
Many thanks to Robert Simons for this question:
"I am exactly $n$ times my daughter's age. In $m$ years I shall
be exactly $(n-1)$ times her age. In $m^2$ years I shall be exactly
$(n-2)$ times her age. After that I shall never again be an exact
multiple of her age. Ages, $n$ and $m$ are all whole numbers. How
old am I?
Now suppose there is some wishful thinking in the above
assertion and I have to admit to being older, and indeed that I
will be an exact multiple of her age in $m^3$ years. How old does
this make me?"