Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
Investigate the numbers that come up on a die as you roll it in the
direction of north, south, east and west, without going over the
path it's already made.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Investigate the different ways you could split up these rooms so
that you have double the number.
An investigation that gives you the opportunity to make and justify
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
If the answer's 2010, what could the question be?
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?
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 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!
Bernard Bagnall describes how to get more out of some favourite
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
This activity asks you to collect information about the birds you
see in the garden. Are there patterns in the data or do the birds
seem to visit randomly?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
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?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
In my local town there are three supermarkets which each has a
special deal on some products. If you bought all your shopping in
one shop, where would be the cheapest?
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Investigate what happens when you add house numbers along a street
in different ways.
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
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
If I use 12 green tiles to represent my lawn, how many different
ways could I arrange them? How many border tiles would I need each
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?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
How many tiles do we need to tile these patios?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
Why does the tower look a different size in each of these pictures?
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 how many ways can you stack these rods, following the rules?
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?