Counting

How many different ways can you arrange the officers in a square?

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?

In how many ways can you give change for a ten pence piece?

Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?

Can you explain how this card trick works?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

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?

What is the largest number of digits that could be erased from this 1000-digit number, to get a surprising result?