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?
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
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.
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Use the clues about the symmetrical properties of these letters to
place them on the grid.
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
Ben has five coins in his pocket. How much money might he have?
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?
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 the information to find out which cards I have used?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
In how many ways can you stack these rods, following the rules?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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 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?
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
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!
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you substitute numbers for the letters in these sums?
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 make square numbers by adding two prime numbers together?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
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?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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!