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?
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?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a 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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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 triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What is the greatest number of squares you can make by overlapping three squares?
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.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
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 use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Can you find all the different triangles on these peg boards, and find their angles?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
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?
Choose a symbol to put into the number sentence.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
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 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.
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. . . .
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
An interactive activity for one to experiment with a tricky tessellation
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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 train building game for two players. Can you be the one to complete the train?
A game in which players take it in turns to choose a number. Can you block your opponent?
Train game for an adult and child. Who will be the first to make the train?