How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
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 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?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
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?
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!
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
These practical challenges are all about making a 'tray' and covering it with paper.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
This challenge is about finding the difference between numbers which have the same tens digit.
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
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.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
My coat has three buttons. How many ways can you find to do up all
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.