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?

Number problems at primary level that require careful consideration.

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?

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

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.

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

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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

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

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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?

There were 22 legs creeping across the web. How many flies? How many spiders?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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?

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?

Can you complete this jigsaw of the multiplication square?

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?

This number has 903 digits. What is the sum of all 903 digits?

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?

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

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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?

Number problems at primary level that may require determination.

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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Can you replace the letters with numbers? Is there only one solution in each case?

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

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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?

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

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

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?