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.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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?
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?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
What is the best way to shunt these carriages so that each train can continue its journey?
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?
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?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?
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 it up?
How many different triangles can you make on a circular pegboard that has nine pegs?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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.
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
Can you picture where this letter "F" will be on the grid if you flip it in these different ways?
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
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?
Have a go at this 3D extension to the Pebbles problem.
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?
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
Can you work out what kind of rotation produced this pattern of pegs in our pegboard?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Can you find ways of joining cubes together so that 28 faces are visible?
What is the greatest number of squares you can make by overlapping three squares?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
In how many ways can you fit all three pieces together to make shapes with line symmetry?
I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
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.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?