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.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
Can you mentally fit the 7 SOMA pieces together to make a cube? Can
you do it in more than one way?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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 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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after
every cut you can rearrange the pieces before cutting straight
through, can you do it in fewer?
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
Can you make a 3x3 cube with these shapes made from small cubes?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of the rocket?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Exchange the positions of the two sets of counters in the least possible number of moves
Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface. . . .
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of the telescope and microscope?