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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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 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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
An activity making various patterns with 2 x 1 rectangular tiles.
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.?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
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?
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?
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Can you find all the different ways of lining up these Cuisenaire
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 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?
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.
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
How many triangles can you make on the 3 by 3 pegboard?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
In how many ways can you stack these rods, following the rules?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
In this matching game, you have to decide how long different events take.