If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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.
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Find all the numbers that can be made by adding the dots on two dice.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This dice train has been made using specific rules. How many different trains can you make?
What happens when you try and fit the triomino pieces into these
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you cover the camel with these pieces?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
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 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?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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 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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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
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!
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?
Ben has five coins in his pocket. How much money might he have?
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?
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.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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!
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
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?
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?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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.
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?
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?