Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Can you substitute numbers for the letters in these sums?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
These two group activities use mathematical reasoning - one is numerical, one geometric.
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?
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?
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?
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?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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 your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
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.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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 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?
Can you replace the letters with numbers? Is there only one solution in each case?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you use the information to find out which cards I have used?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Ben has five coins in his pocket. How much money might he have?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.