Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
How many right angles can you make using two sticks?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Move just three of the circles so that the triangle faces in the
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Match the halves.
Work out the fractions to match the cards with the same amount of
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
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....?
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
How many times in twelve hours do the hands of a clock form a right
angle? Use the interactivity to check your answers.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Exchange the positions of the two sets of counters in the least possible number of moves
An interactive activity for one to experiment with a tricky tessellation
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
How many different rhythms can you make by putting two drums on the
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Try this interactive strategy game for 2
A variant on the game Alquerque
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Work out how to light up the single light. What's the rule?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
A collection of our favourite pictorial problems, one for each day
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?