Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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?
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.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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.
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?
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.
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?
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.
How many trapeziums, of various sizes, are hidden in this picture?
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?
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?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
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?
Can you use this information to work out Charlie's house number?
Can you find out in which order the children are standing in this line?
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?
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?
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.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Investigate the different ways you could split up these rooms so that you have double the number.
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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.
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?
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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.
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?
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?
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.