On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
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!
Can you replace the letters with numbers? Is there only one
solution in each case?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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!
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?
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?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
What is happening at each box in these machines?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Use the information to work out how many gifts there are in each
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
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 group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?