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?
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
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
What is the best way to shunt these carriages so that each train
can continue its journey?
Use the clues to colour each square.
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
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?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
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?
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?
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?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
How many different rhythms can you make by putting two drums on the
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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 DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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.
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.
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.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue.
She wants to fit them together to make a cube so that each colour shows on each face just once.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
How many trains can you make which are the same length as Matt's,
using rods that are identical?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
How many different triangles can you make on a circular pegboard that has nine pegs?
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....?
Can you find all the different ways of lining up these Cuisenaire
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
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?
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 your way through the grid starting at 2 and following these
operations. What number do you end on?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?