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 cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
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 shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
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
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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 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?
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?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of these rabbits?
I've made some cubes and some cubes with holes in. This challenge
invites you to explore the difference in the number of small cubes
I've used. Can you see any patterns?
Can you fit the tangram pieces into the outline of this sports car?
Here are the six faces of a cube - in no particular order. Here are
three views of the cube. Can you deduce where the faces are in
relation to each other and record them on the net of this cube?
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?
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of Mai Ling?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Can you fit the tangram pieces into the outline of these convex shapes?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you make a 3x3 cube with these shapes made from small cubes?
Can you cut up a square in the way shown and make the pieces into a
Which of the following cubes can be made from these nets?
Can you fit the tangram pieces into the outline of Little Ming?
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.
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of this junk?