Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
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.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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?
In how many ways can you stack these rods, following the rules?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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!
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?
Can you use this information to work out Charlie's house number?
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?
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?
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?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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 ...?
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?
What could the half time scores have been in these Olympic hockey matches?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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.
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.
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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?
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.
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.
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?
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!
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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.?
How many trapeziums, of various sizes, are hidden in this picture?
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?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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?
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.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
You have 5 darts and your target score is 44. How many different ways could you score 44?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?