What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you replace the letters with numbers? Is there only one
solution in each case?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
Given the products of adjacent cells, can you complete this Sudoku?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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 seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
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?
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?
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?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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 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.
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!
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?
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
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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.
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?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.