Permutations

problem
And so on and so on

Age

11 to 14

Challenge level

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?
problem
Thank your lucky stars

Age

14 to 16

Challenge level

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand corner of the grid?
problem
Factoring a million

Age

14 to 16

Challenge level

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
problem
Euromaths

Age

11 to 14

Challenge level

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 a 5x5 array?
problem
Flagging

Age

11 to 14

Challenge level

How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?
problem
Painting cubes

Age

11 to 14

Challenge level

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?
article
Card shuffle

This article for students and teachers tries to think about how long would it take someone to create every possible shuffle of a pack of cards, with surprising results.
article
Ding dong bell

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.