Try out the lottery that is played in a far-away land. What is the
chance of winning?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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 different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
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 6 in the circles so that each number is the
difference between the two numbers just below it.
Use the clues to colour each square.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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....?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Can you find all the different ways of lining up these Cuisenaire
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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 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 different rhythms can you make by putting two drums on the
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
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 is the best way to shunt these carriages so that each train
can continue its journey?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
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?
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
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.
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?
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?
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?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Investigate the different ways you could split up these rooms so
that you have double the number.