Permutations

problem

Voting paradox

Age

14 to 18

Challenge level

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?
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

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

Ip?

Age

16 to 18

Challenge level

Seventh challenge cipher
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

Even up

Age

11 to 14

Challenge level

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?
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?