Combinations

problem
Domino sorting

Age

5 to 7

Challenge level

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
problem
Triangle animals

Age

5 to 7

Challenge level

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
problem
Colour building

Age

11 to 14

Challenge level

Using only the red and white rods, how many different ways are there to make up the other rods?
problem
Patchwork quilt

Age

7 to 14

Challenge level

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?
problem
Three ball line up

Age

5 to 7

Challenge level

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
problem
Two and one

Age

5 to 7

Challenge level

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
problem
The twelve pointed star game

Age

7 to 11

Challenge level

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
problem
Nineteen hexagons

Age

5 to 7

Challenge level

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
problem
Cuisenaire counting

Age

5 to 7

Challenge level

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
problem
Butterfly cards

Age

7 to 11

Challenge level

Four children were sharing a set of twenty-four butterfly cards. Are there any cards they all want? Are there any that none of them want?