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.
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 information?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This challenge is about finding the difference between numbers which have the same tens digit.
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 jugs.
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?
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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.
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements 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?
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?
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?
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 the buttons?
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.
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Can you use this information to work out Charlie's house 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 find out in which order the children are standing in this line?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
Find all the numbers that can be made by adding the dots on two dice.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .