Combinations

problem
Mrs Beeswax

Age

5 to 7

Challenge level

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
problem
Cross-country race

Age

14 to 16

Challenge level

Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?
problem
1 step 2 step

Age

11 to 14

Challenge level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
problem
Add 3 dice

Age

7 to 11

Challenge level

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?
problem
Wag worms

Age

7 to 11

Challenge level

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
problem
Waiting for blast off

Age

7 to 11

Challenge level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
problem
A rod and a pole

Age

7 to 11

Challenge level

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
problem
Map folding

Age

7 to 11

Challenge level

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
problem
Calendar cubes

Age

7 to 11

Challenge level

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
problem
Team scream

Age

7 to 11

Challenge level

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?