Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
Can you find what the last two digits of the number $4^{1999}$ are?
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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" .
A game that tests your understanding of remainders.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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. . . .
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.
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?
Find the highest power of 11 that will divide into 1000! exactly.
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?
The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.
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.
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.
This problem is designed to help children to learn, and to use, the two and three times tables.
What is the remainder when 2^{164}is divided by 7?
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?
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.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
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?
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?
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 the next number in this pattern: 3, 7, 19, 55 ...
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
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?
Here is a picnic that Chris and Michael are going to share equally. Can you tell us what each of them will have?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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.
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 Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
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 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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
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?