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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
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 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.
An activity making various patterns with 2 x 1 rectangular tiles.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
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.
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....?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Can you find all the different ways of lining up these Cuisenaire
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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 triangles can you make on a circular pegboard that has nine pegs?
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.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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
In this matching game, you have to decide how long different events take.
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.
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
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
In how many ways can you stack these rods, following the rules?
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?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.