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?
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
Congratulations to Fok Chi Kwong from Yuen Long Merchants
Association Secondary School, Hong Kong on this solution.
We may find the required polynomial by starting from the
$$x = 1 + \sqrt 2 + \sqrt 3$$.
Squaring both sides and simplifying, we get
\[x - 1 = \sqrt 2+ \sqrt 3 \] \[x^2 - 2x + 1 = 5 + 2\sqrt 6 \]
\[ x^2 - 2x - 4 = 2\sqrt 6 \] \[(x^2 - 2x - 4)^2 = 24 \] \[x^4 -
4x^3 + 4x^2 - 8x^2 + 16x + 16 = 24 \] \[x^4 - 4x^3 - 4x^2 + 16x - 8
= 0 \]
Thus $p(x) = x^4 - 4x^3 - 4x^2 + 16x - 8$ is the required
Tony Cardell, State College Area High School, PA, USA, also sent
in a good solution.