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?
Are these domino games fair? Can you explain why or why not?
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
Number problems at primary level that require careful consideration.
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.
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?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Find a great variety of ways of asking questions which make 8.
Investigate the different distances of these car journeys and find out how long they take.
What is the sum of all the three digit whole numbers?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Can you substitute numbers for the letters in these sums?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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 is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
If you have only four weights, where could you place them in order to balance this equaliser?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
Here is a chance to play a version of the classic Countdown Game.
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.
If the answer's 2010, what could the question be?
How would you count the number of fingers in these pictures?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
What is happening at each box in these machines?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Number problems at primary level to work on with others.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?