Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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.
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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?
How many models can you find which obey these rules?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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.
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?
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 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?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Can you fill in the empty boxes in the grid with the right shape and colour?
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?
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 town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Can you draw a square in which the perimeter is numerically equal to the area?
This activity investigates how you might make squares and pentominoes from Polydron.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
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?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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!
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Investigate the different ways you could split up these rooms so that you have double the number.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
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.
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?