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 arrange 5 different digits (from 0 - 9) in the cross in the way described?
These two group activities use mathematical reasoning - one is numerical, one geometric.
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?
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!
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
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?
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.
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.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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.
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?
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 Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
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?
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!
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?
Can you substitute numbers for the letters in these sums?
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?
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?
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?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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.
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
Can you make square numbers by adding two prime numbers together?
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.
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
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.
Can you use the information to find out which cards I have used?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?
If the answer's 2010, what could the question be?