Permutations
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?
How many ways can you paint this wall with four different colours?
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
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
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
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
Six times five
Age
11 to 14
Challenge level
How many six digit numbers are there which DO NOT contain a 5?
problem
396
Age
14 to 16
Challenge level
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.
problem
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
Master Minding
Age
11 to 14
Challenge level
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?