Given the products of adjacent cells, can you complete this Sudoku?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two
digit numbers are multiplied to give a four digit number, so that
the expression is correct. How many different solutions can you
Here is a chance to play a version of the classic Countdown Game.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Can you complete this jigsaw of the multiplication square?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do 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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
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?
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.
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.
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 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.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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!
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.