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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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!
Can you substitute numbers for the letters in these sums?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Number problems at primary level that require careful consideration.
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!
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Can you replace the letters with numbers? Is there only one solution in each case?
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.
Can you find the chosen number from the grid using the clues?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Can you make square numbers by adding two prime numbers together?
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.
Ben has five coins in his pocket. How much money might he have?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
You have 5 darts and your target score is 44. How many different ways could you score 44?
Use these head, body and leg pieces to make Robot Monsters which are different heights.