Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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 work out what a ziffle is on the planet Zargon?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
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?
Number problems at primary level that require careful consideration.
56 406 is the product of two consecutive numbers. What are these
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 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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is it?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
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?
Number problems at primary level that may require determination.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
This number has 903 digits. What is the sum of all 903 digits?
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?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
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!
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 score 100 by throwing rings on this board? Is there more
than way to do it?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
What is happening at each box in these machines?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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!
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Can you complete this jigsaw of the multiplication square?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?