Painting Cubes

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?

Tri-colour

Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?

Permute It

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 resulting numbers.

Euromaths

Stage: 3 Challenge Level:
You might like to look at Counting on Letters before you try this problem.

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?

 E U R O M U R O M A R O M A T O M A T H M A T H S

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.