Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
An investigation that gives you the opportunity to make and justify
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
What happens when you round these three-digit numbers to the nearest 100?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
What happens when you round these numbers to the nearest whole number?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Have a go at balancing this equation. Can you find different ways of doing it?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?