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?
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 models can you find which obey these rules?
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.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue.
She wants to fit them together to make a cube so that each colour shows on each face just once.
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.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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
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?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Use the clues to colour each square.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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 cover the camel with these pieces?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How many different rhythms can you make by putting two drums on the
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
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?
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
What happens when you try and fit the triomino pieces into these
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.
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?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
An activity making various patterns with 2 x 1 rectangular tiles.
Take three differently coloured blocks - maybe red, yellow and
blue. Make a tower using one of each colour. How many different
towers can you make?
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
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.
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?
Explore the different snakes that can be made using 5 cubes.
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
My coat has three buttons. How many ways can you find to do up all
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?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.