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?
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?
Hover your mouse over the counters to see which ones will be removed. Click to remove 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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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 1 to 8 into the circles so that the four calculations are correct?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Can you find all the different ways of lining up these Cuisenaire rods?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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....?
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?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Find out what a "fault-free" rectangle is and try to make some of your own.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
If you have only four weights, where could you place them in order to balance this equaliser?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Choose a symbol to put into the number sentence.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you complete this jigsaw of the multiplication square?
Here is a chance to play a version of the classic Countdown Game.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
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 for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
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?
An interactive activity for one to experiment with a tricky tessellation
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.
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.
Work out the fractions to match the cards with the same amount of money.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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.
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Use the interactivity or play this dice game yourself. How could you make it fair?