Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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.
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.
Can you substitute numbers for the letters in these sums?
Ben has five coins in his pocket. How much money might he have?
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.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
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!
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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.
Find all the numbers that can be made by adding the dots on two dice.
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?
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?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you use the information to find out which cards I have used?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
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?
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?