Find all the numbers that can be made by adding the dots on two dice.
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
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.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
This challenge is about finding the difference between numbers which have the same tens digit.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
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. . . .
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
Can you substitute numbers for the letters in these sums?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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!
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?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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.
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Ben has five coins in his pocket. How much money might he have?
Can you make square numbers by adding two prime numbers together?
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!
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?
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?
Number problems at primary level that require careful consideration.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
What could the half time scores have been in these Olympic hockey matches?
Can you use the information to find out which cards I have used?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
This dice train has been made using specific rules. How many different trains can you make?