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?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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 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?
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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 ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
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 many models can you find which obey these rules?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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.
These practical challenges are all about making a 'tray' and covering it with paper.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you find all the different ways of lining up these Cuisenaire
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Find out what a "fault-free" rectangle is and try to make some of
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.