Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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 find?
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?
Can you find what the last two digits of the number $4^{1999}$ are?
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?
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?
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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.
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?
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.
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. . . .
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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.
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
A game that tests your understanding of remainders.
Find a great variety of ways of asking questions which make 8.
Can you work out what a ziffle is on the planet Zargon?
Given the products of adjacent cells, can you complete this Sudoku?
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" .
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
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 happens?
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.
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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 number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
What is the remainder when 2^{164}is divided by 7?
This problem is designed to help children to learn, and to use, the two and three times tables.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
What is the sum of all the three digit whole numbers?
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Here is a chance to play a version of the classic Countdown Game.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?