This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
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?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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!
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?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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?
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 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.
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you substitute numbers for the letters in these sums?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Ben has five coins in his pocket. How much money might he have?
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!
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?
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?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
This dice train has been made using specific rules. How many different trains can you make?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you use the information to find out which cards I have used?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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 use this information to work out Charlie's house number?
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?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?