Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
A game that tests your understanding of remainders.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Here is a chance to play a version of the classic Countdown Game.
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?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Can you complete this jigsaw of the multiplication square?
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 why 2 by 2 could be 5? Can you predict what 2 by 10
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Can you work out what a ziffle is on the planet Zargon?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
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?
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?
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?
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.
Can you replace the letters with numbers? Is there only one
solution in each case?
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 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?
Number problems at primary level that require careful consideration.
Choose a symbol to put into the number sentence.
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Use the information to work out how many gifts there are in each
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
What is happening at each box in these machines?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.