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?
Use the clues to colour each square.
How many trains can you make which are the same length as Matt's, using rods that are identical?
How many different triangles can you make on a circular pegboard that has nine pegs?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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 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.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you find all the different ways of lining up these Cuisenaire
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 different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
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.
Can you cover the camel with these pieces?
How many different rhythms can you make by putting two drums on the
What happens when you try and fit the triomino pieces into these
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
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?
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?
Can you find all the different triangles on these peg boards, and
find their angles?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
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?
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
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
What is the best way to shunt these carriages so that each train
can continue its journey?
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 the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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.
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Find out what a "fault-free" rectangle is and try to make some of
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?
An activity making various patterns with 2 x 1 rectangular tiles.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?