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.
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 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 group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
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.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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 task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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 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.
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?
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 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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This dice train has been made using specific rules. How many different trains can you make?
This task follows on from Build it Up and takes the ideas into three dimensions!
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Investigate the different distances of these car journeys and find out how long they take.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
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?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
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.
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
Can you substitute numbers for the letters in these sums?
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?
These two group activities use mathematical reasoning - one is numerical, one geometric.