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?
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
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?
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?
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 work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
How many different rhythms can you make by putting two drums on 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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Use the clues to colour each square.
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Find out what a "fault-free" rectangle is and try to make some of
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Can you find all the different ways of lining up these Cuisenaire
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
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 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.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
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?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
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.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
How many different triangles can you make on a circular pegboard that has nine pegs?
These practical challenges are all about making a 'tray' and covering it with paper.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Try this matching game which will help you recognise different ways of saying the same time interval.
How many models can you find which obey these rules?