Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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.
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.
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?
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.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
In how many ways can you stack these rods, following the rules?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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 use this information to work out Charlie's house number?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
How many trapeziums, of various sizes, are hidden in this picture?
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 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!
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
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?
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 statements, can you work out how many of each type of rabbit there are in these pens?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
What could the half time scores have been in these Olympic hockey matches?
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.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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!
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.