Combinations

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?
problem

Flagging

Age

11 to 14

Challenge level

2 out of 3

How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?
problem

Semaphore Signals

Age

7 to 11

Challenge level

2 out of 3

Semaphore is a way to signal the alphabet using two flags. You might want to send a message that contains more than just letters. How many other symbols could you send using this code?
problem

Brailler

Age

11 to 14

Challenge level

2 out of 3

The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?