These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
What is the sum of all the three digit whole numbers?
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.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
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 is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
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?
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!
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?
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 your logical reasoning to work out how many cows and how many
sheep there are in each field.
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 number has 903 digits. What is the sum of all 903 digits?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
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
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
What is happening at each box in these machines?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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!
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
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?
Use the information to work out how many gifts there are in each
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?