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?
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.
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
It starts quite simple but great opportunities for number discoveries and patterns!
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 different sets of numbers with at least four members can
you find in the numbers in this box?
If the answer's 2010, what could the question be?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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.
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
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?
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!
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?
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?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
An investigation that gives you the opportunity to make and justify
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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.
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?
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.
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
Investigate what happens when you add house numbers along a street
in different ways.
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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?
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?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
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?
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
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.