Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
How many models can you find which obey these rules?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
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 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?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Find out about Magic Squares in this article written for students. Why are they magic?!
Find out what a "fault-free" rectangle is and try to make some of
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This task follows on from Build it Up and takes the ideas into three dimensions!
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
If you had 36 cubes, what different cuboids could you make?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
A Sudoku with clues as ratios or fractions.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
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?
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....?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?