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?
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
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
An activity making various patterns with 2 x 1 rectangular tiles.
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 ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
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.
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?
These practical challenges are all about making a 'tray' and covering it with paper.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Investigate the different ways you could split up these rooms so
that you have double the number.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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.
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!