Permutations

problem
Favourite

Six Times Five

Age

11 to 14

Challenge level

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

Chances Are

Age

14 to 16

Challenge level

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

Bell Ringing

Age

11 to 14

Challenge level

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?
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?
problem

Ip?

Age

16 to 18

Challenge level

Seventh challenge cipher
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 5×5 array?
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

Oranges and Lemons, Say the Bells of St Clement's

Age

11 to 14

Challenge level

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

Colourful Tiles

Age

11 to 14

Challenge level

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