How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many different symmetrical shapes can you make by shading triangles or squares?
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 triangles can you make on a circular pegboard that has nine pegs?
Try this interactive strategy game for 2
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?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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 remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
An extension of noughts and crosses in which the grid is enlarged
and the length of the winning line can to altered to 3, 4 or 5.
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
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?
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!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
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?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
What is the best way to shunt these carriages so that each train
can continue its journey?
A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
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?
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?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
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?
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
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
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?
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?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
A game for two players on a large squared space.
Exchange the positions of the two sets of counters in the least possible number of moves
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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.
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?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?