Combinations

problem
Favourite

Elevenses

Age

11 to 14

Challenge level

1 out of 3

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
problem
Favourite

1 Step 2 Step

Age

11 to 14

Challenge level

2 out of 3

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
Favourite

Take Three From Five

Age

11 to 16

Challenge level

2 out of 3

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Favourite

Crossing the Bridge

Age

11 to 18

Challenge level

2 out of 3

Four friends must cross a bridge. How can they all cross it in just 17 minutes?
problem
Favourite

Chances Are

Age

14 to 16

Challenge level

1 out of 3

Which of these games would you play to give yourself the best possible chance of winning a prize?
problem
Favourite

Teams

Age

16 to 18

Challenge level

1 out of 3

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.
problem

Lesser Digits

Age

11 to 14

Challenge level

1 out of 3

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
problem

Sam Again

Age

11 to 14

Challenge level

1 out of 3

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.
problem

Patchwork Quilt

Age

7 to 14

Challenge level

1 out of 3

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

Cereal Packets

Age

7 to 11

Challenge level

2 out of 3

How can you put five cereal packets together to make different shapes if you must put them face-to-face?