Working systematically

problem
Page numbers

Age

7 to 11

Challenge level

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
problem
Heads and feet

Age

5 to 7

Challenge level

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
problem
Football crazy hockey mad

Age

11 to 14

Challenge level

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.
problem
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
In a box

Age

14 to 16

Challenge level

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
problem
Tree tops

Age

14 to 16

Challenge level

Can you make sense of information about trees in order to maximise the profits of a forestry company?
problem
Pattern of islands

Age

11 to 14

Challenge level

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
problem
Master minding

Age

11 to 14

Challenge level

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?
problem
A right Charlie

Age

7 to 11

Challenge level

Can you use this information to work out Charlie's house number?
problem
CD Heaven

Age

14 to 16

Challenge level

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?