Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few 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!
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
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. . . .
Can you substitute numbers for the letters in these sums?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
My coat has three buttons. How many ways can you find to do up all the buttons?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you find all the different triangles on these peg boards, and find their angles?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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!
Ben has five coins in his pocket. How much money might he have?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
Can you make square numbers by adding two prime numbers together?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?