Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Can you find the chosen number from the grid using the clues?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
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?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Can you replace the letters with numbers? Is there only one solution in each case?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
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?
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
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.
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?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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!
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
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.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Can you make square numbers by adding two prime numbers together?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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?
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
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?