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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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....?
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?
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 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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you find all the different ways of lining up these Cuisenaire
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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 triangles can you make on a circular pegboard that has nine pegs?
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?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
An activity making various patterns with 2 x 1 rectangular tiles.
What is the best way to shunt these carriages so that each train
can continue its journey?
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 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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
These practical challenges are all about making a 'tray' and covering it with paper.
How many triangles can you make on the 3 by 3 pegboard?
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?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
In this matching game, you have to decide how long different events take.
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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
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?
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.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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?
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
Find out what a "fault-free" rectangle is and try to make some of
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
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Investigate the different ways you could split up these rooms so
that you have double the number.