Use the interactivity or play this dice game yourself. How could
you make it fair?
Play a dice game of chance
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Play this well-known game against the computer where each player is
equally likely to choose scissors, paper or rock. Why not try the
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
How many right angles can you make using two sticks?
Work out the fractions to match the cards with the same amount of
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
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....?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
A variant on the game Alquerque
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!
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?
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Move just three of the circles so that the triangle faces in the
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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?
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 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?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Match the halves.
How many different rhythms can you make by putting two drums on the
An interactive activity for one to experiment with a tricky tessellation
Exchange the positions of the two sets of counters in the least possible number of moves
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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!
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A tool for generating random integers.
Use this animation to experiment with lotteries. Choose how many
balls to match, how many are in the carousel, and how many draws to
make at once.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Choose a symbol to put into the number sentence.
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?