Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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 many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
Can you fit the tangram pieces into the outline of this plaque design?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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 fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outline of the rocket?
Can you cut up a square in the way shown and make the pieces into a
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you fit the tangram pieces into the outline of this junk?
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of Mai Ling?
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?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of these rabbits?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you fit the tangram pieces into the outline of these convex shapes?
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?
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outlines of the candle and sundial?
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 shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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.
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outline of this sports car?
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?
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 fit the tangram pieces into the outlines of the chairs?
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 fit the tangram pieces into the outline of this goat and giraffe?
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?
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
Here's a simple way to make a Tangram without any measuring or
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?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?