Combinations

problem
Sweets in a box

Age

7 to 11

Challenge level

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
problem
Bean bags for Bernard's bag

Age

7 to 11

Challenge level

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
problem
Ice cream

Age

7 to 11

Challenge level

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
problem
It figures

Age

7 to 11

Challenge level

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
problem
Room doubling

Age

7 to 11

Challenge level

Investigate the different ways you could split up these rooms so that you have double the number.
problem
Train carriages

Age

5 to 11

Challenge level

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
problem
New house

Age

7 to 11

Challenge level

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?
problem
Dice and spinner numbers

Age

7 to 11

Challenge level

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
problem
Sending cards

Age

7 to 11

Challenge level

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
problem
Street party

Age

7 to 11

Challenge level

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.