Combinations

problem
Zargon glasses

Age

7 to 11

Challenge level

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
problem
Octa space

Age

7 to 11

Challenge level

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
problem
Prison cells

Age

7 to 11

Challenge level

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
problem
Briefcase lock

Age

5 to 7

Challenge level

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
problem
Football crazy hockey mad

Age

11 to 14

Challenge level

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.
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
Flight of the Flibbins

Age

11 to 14

Challenge level

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
Pattern of islands

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?
problem
Domino tetrads

Age

11 to 14

Challenge level

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