Combinations

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

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

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

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?

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?

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

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?

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

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

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