Working systematically

problem
Favourite

Over-Booking

Age

16 to 18

Challenge level

3 out of 3

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 2% of flights are over-booked?
problem

Counting on Letters

Age

11 to 14

Challenge level

1 out of 3

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
problem

Purr-Fection

Age

16 to 18

Challenge level

1 out of 3

What is the smallest perfect square that ends with the four digits 9009?
problem

Plum Tree

Age

14 to 18

Challenge level

1 out of 3

Label this plum tree graph to make it totally magic!
problem

W Mates

Age

16 to 18

Challenge level

1 out of 3

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
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

Magnetic Personality

Age

7 to 16

Challenge level

1 out of 3

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
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

How Old Are the Children?

Age

11 to 14

Challenge level

2 out of 3

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
problem

Ones Only

Age

11 to 14

Challenge level

2 out of 3

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.