How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
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 models can you find which obey these rules?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
In how many ways can you stack these rods, following the rules?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Can you find all the different ways of lining up these Cuisenaire
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?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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
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?
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 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?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
An activity making various patterns with 2 x 1 rectangular tiles.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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.
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
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?
If you had 36 cubes, what different cuboids could you make?
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
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.
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Can you draw a square in which the perimeter is numerically equal
to the area?