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?
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?
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
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
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 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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Use the information to work out how many gifts there are in each
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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.
What is happening at each box in these machines?
Amy has a box containing domino pieces but she does not think it is
a complete set. She has 24 dominoes in her box and there are 125
spots on them altogether. Which of her domino pieces are missing?
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
How would you count the number of fingers in these pictures?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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!
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
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.
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 at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you replace the letters with numbers? Is there only one
solution in each case?