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.
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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.
Can you use the information to find out which cards I have used?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
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?
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.?
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?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Can you find the chosen number from the grid using the clues?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
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.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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 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?
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?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
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.
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?
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?
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?
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!
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Investigate the different ways you could split up these rooms so
that you have double the number.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
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
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
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?