Combinations

problem
Favourite

Take Three From Five

Age

11 to 16

Challenge level

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

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

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

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

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

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

Satnav Dilemma

Age

11 to 14

Challenge level

How many routes are there in this diagram from S to T?
problem

Negative Dice

Age

11 to 14

Challenge level

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
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

Making 11p

Age

11 to 14

Challenge level

How many ways are there to make 11p using 1p, 2p and 5p coins?