Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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.
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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.
Find all the numbers that can be made by adding the dots on two dice.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
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?
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.
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below 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?
An investigation that gives you the opportunity to make and justify predictions.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
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 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?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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!
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?
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?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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?
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
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?