Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Place the numbers 1 to 6 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 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?
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 trains can you make which are the same length as Matt's, using rods that are identical?
Use the clues to colour each square.
Can you find all the different ways of lining up these Cuisenaire
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
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 ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How many different rhythms can you make by putting two drums on the
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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?
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?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Find out what a "fault-free" rectangle is and try to make some of
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.
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
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?