Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
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. . . .
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?
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.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.
Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .
Here is a picnic that Chris and Michael are going to share equally. Can you tell us what each of them will have?
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?
Can you find what the last two digits of the number $4^{1999}$ are?
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.
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 article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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!?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
What is the remainder when 2^{164}is divided by 7?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
This problem is designed to help children to learn, and to use, the two and three times tables.
Resources to support understanding of multiplication and division through playing with number.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
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?
Can you work out what a ziffle is on the planet Zargon?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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.
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
This number has 903 digits. What is the sum of all 903 digits?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
A game that tests your understanding of remainders.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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?
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.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Given the products of adjacent cells, can you complete this Sudoku?