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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Choose a symbol to put into the number sentence.
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?
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!
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Here is a chance to play a version of the classic Countdown Game.
If you have only four weights, where could you place them in order to balance this equaliser?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Delight your friends with this cunning trick! Can you explain how it works?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Find the sum of all three-digit numbers each of whose digits is odd.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
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?
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?
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
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!
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.
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?
There are nasty versions of this dice game but we'll start with the nice ones...
A game for 2 players. Practises subtraction or other maths operations knowledge.
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?
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?
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?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Can you be the first to complete a row of three?
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 explain how this card trick works?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?