Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
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!
Find all the numbers that can be made by adding the dots on two dice.
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.
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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 put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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?
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?
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?
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!
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 how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
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?
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?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Can you hang weights in the right place to make the equaliser balance?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
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?
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?
Ben has five coins in his pocket. How much money might he have?
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.
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
These two group activities use mathematical reasoning - one is numerical, one geometric.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.