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There are **17** NRICH Mathematical resources connected to **Permutations**, you may find related items under Decision mathematics and combinatorics.

Problem
Primary curriculum
Secondary curriculum
### Six Times Five

How many six digit numbers are there which DO NOT contain a 5?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chances Are

Which of these games would you play to give yourself the best possible chance of winning a prize?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### 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.

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Oranges and Lemons, Say the Bells of St Clement's

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bell Ringing

Suppose you are a bellringer. Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Even Up

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Voting Paradox

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 396

The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### 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.

Age 11 to 18

Problem
Primary curriculum
Secondary curriculum
### Master Minding

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### And So on and So On

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Thank Your Lucky Stars

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factoring a Million

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Euromaths

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flagging

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 11 to 14

Challenge Level