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. . . .

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?

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.

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.

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?

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 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.

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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.

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?

This problem is designed to help children to learn, and to use, the two and three times tables.

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?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

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. . . .

Number problems at primary level that may require determination.

56 406 is the product of two consecutive numbers. What are these two numbers?

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?

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!?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Are these statements always true, sometimes true or never true?

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?

Resources to support understanding of multiplication and division through playing with number.

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?

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?

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?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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?

Have a go at balancing this equation. Can you find different ways of doing it?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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.

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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.

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Use the information to work out how many gifts there are in each pile.

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?