Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
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.
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?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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!
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
In how many ways can you stack these rods, following the rules?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you use this information to work out Charlie's house number?
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?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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?
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.
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.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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.?
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?
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.
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?
What could the half time scores have been in these Olympic hockey matches?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
How many trapeziums, of various sizes, are hidden in this picture?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
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.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?