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?
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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!
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
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?
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.
This task follows on from Build it Up and takes the ideas into three dimensions!
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
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?
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?
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?
This challenge is about finding the difference between numbers which have the same tens digit.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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 task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
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?
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?
Ben has five coins in his pocket. How much money might he have?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
My coat has three buttons. How many ways can you find to do up all
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
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.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Can you use this information to work out Charlie's house number?
Can you find out in which order the children are standing in this
Can you substitute numbers for the letters in these sums?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Find all the numbers that can be made by adding the dots on two dice.
Use these head, body and leg pieces to make Robot Monsters which are different heights.