Combinations

problem

Colourful Tiles

Age

11 to 14

Challenge level

1 out of 3

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

Unequal Exam

Age

11 to 14

Challenge level

1 out of 3

120 students sit an exam with 100 marks available. What is the smallest number of pairs that are awarded the same mark?
problem

Pattern of Islands

Age

11 to 14

Challenge level

2 out of 3

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
problem

Flight of the Flibbins

Age

11 to 14

Challenge level

2 out of 3

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to the new planet?
problem

Clocked

Age

11 to 14

Challenge level

2 out of 3

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
problem

Domino Tetrads

Age

11 to 14

Challenge level

3 out of 3

Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?
problem

Even Up

Age

11 to 14

Challenge level

3 out of 3

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

Coins

Age

11 to 14

Challenge level

3 out of 3

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
problem

Almost Constant Digits

Age

11 to 14

Challenge level

3 out of 3

How many 10-digit numbers containing only 1s, 2s and 3s can you write?
problem

Nine or Ten?

Age

11 to 14

Challenge level

3 out of 3

Is a score of 9 more likely than a score of 10 when you roll three dice?