Can you find all the different ways of lining up these Cuisenaire
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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....?
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?
Use the clues to colour each square.
What happens when you try and fit the triomino pieces into these
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you cover the camel with these pieces?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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?
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.
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
These practical challenges are all about making a 'tray' and covering it with paper.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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.
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
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?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
How many models can you find which obey these rules?