Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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 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?
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?
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.
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?
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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 task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you find all the different ways of lining up these Cuisenaire rods?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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!
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!
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
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.
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.
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?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?