Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Choose a symbol to put into the number sentence.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
If you have only four weights, where could you place them in order to balance this equaliser?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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?
There are nasty versions of this dice game but we'll start with the nice ones...
Here is a chance to play a version of the classic Countdown Game.
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?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
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.
Delight your friends with this cunning trick! Can you explain how it works?
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!
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Can you substitute numbers for the letters in these sums?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
An environment which simulates working with Cuisenaire rods.
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?
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?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
Can you be the first to complete a row of three?