Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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 the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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 lots of different methods to find out what the shapes are worth - how many can you find?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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?
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 task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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!
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?
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 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.
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
How many trapeziums, of various sizes, are hidden in this picture?
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
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 seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Investigate the different ways you could split up these rooms so that you have double the number.
What could the half time scores have been in these Olympic hockey matches?
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?