Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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!
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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!
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge is about finding the difference between numbers which have the same tens digit.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Find all the numbers that can be made by adding the dots on two dice.
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Ben has five coins in his pocket. How much money might he have?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
My coat has three buttons. How many ways can you find to do up all
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?