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?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
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.
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.?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?
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?
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?
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?
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.
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
How many triangles can you make on the 3 by 3 pegboard?
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?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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....?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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.
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?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
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?
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!
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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 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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?