48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Number problems at primary level that may require determination.

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?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Can you make square numbers by adding two prime numbers together?

Got It game for an adult and child. How can you play so that you know you will always win?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Number problems at primary level to work on with others.

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

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

An investigation that gives you the opportunity to make and justify predictions.

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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.

How many different sets of numbers with at least four members can you find in the numbers in this box?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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

Can you work out some different ways to balance this equation?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?