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
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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 use this information to work out Charlie's house number?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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 many different triangles can you make on a circular pegboard
that has nine pegs?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Can you find all the different ways of lining up these Cuisenaire
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many different symmetrical shapes can you make by shading triangles or squares?
How many models can you find which obey these rules?
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?
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.
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?
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?
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.