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?
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?
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
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.
The pages of my calendar have got mixed up. Can you sort them out?
Try this matching game which will help you recognise different ways of saying the same time interval.
In this matching game, you have to decide how long different events take.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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.
Can you find all the different triangles on these peg boards, and
find their angles?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Find out what a "fault-free" rectangle is and try to make some of
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you find all the different ways of lining up these Cuisenaire
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
How many different triangles can you make on a circular pegboard that has nine pegs?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
This challenge extends the Plants investigation so now four or more children are involved.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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....?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Can you cover the camel with these pieces?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.