Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
56 406 is the product of two consecutive numbers. What are these
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Can you complete this jigsaw of the multiplication square?
What is the sum of all the three digit whole numbers?
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?
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?
Here is a chance to play a version of the classic Countdown Game.
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
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 work out what a ziffle is on the planet Zargon?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
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?
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.
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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?
Use the information to work out how many gifts there are in each
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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!
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
This problem is designed to help children to learn, and to use, the two and three times tables.
Can you work out some different ways to balance this equation?