Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
What is the sum of all the three digit whole numbers?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?
In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Use the information to work out how many gifts there are in each pile.
Find the sum of all three-digit numbers each of whose digits is odd.
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
What is happening at each box in these machines?
The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
This number has 903 digits. What is the sum of all 903 digits?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
Find the next number in this pattern: 3, 7, 19, 55 ...
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
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?
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?
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!
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?