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?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Can you make square numbers by adding two prime numbers together?
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?
Number problems at primary level to work on with others.
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.
Number problems at primary level that may require resilience.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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!
Use the information to work out how many gifts there are in each pile.
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
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 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?
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!
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.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
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?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
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.
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.
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?
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.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Investigate the different distances of these car journeys and find out how long they take.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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 sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?