Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?
Six points are arranged in space so that no three are collinear.
How many line segments can be formed by joining the points in
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in
every possible order to give 5 digit numbers. Find the sum of the
How many ways can you write the word EUROMATHS by starting at
the top left hand corner and taking the next letter by stepping one
step down or one step to the right in this array?
Thank you to Henriett Keri from Miskolc in Hungary for bringing
this task for discussion at our EuroMaths conference, with
Josephine Burgess from Bedfordshire in England, and Inga Bendtsen
and Karina Leth Hansen from Aarhus in Denmark. The task was
contributed by Eva Pinter Kovacsne from Tiszaujvaros, Hungary.