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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
This challenge is about finding the difference between numbers which have the same tens digit.
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?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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 you make?
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.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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.
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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 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 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.
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?
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?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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!
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?
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.
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
My coat has three buttons. How many ways can you find to do up all the buttons?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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 ...?
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?
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?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?