On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens 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 resilience.

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?

How will you work out which numbers have been used to create this multiplication square?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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?

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?

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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

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

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

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

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

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?

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

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Number problems at primary level to work on with others.

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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

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?

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

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

Can you find different ways of creating paths using these paving slabs?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

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

"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 ...?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

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?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Can you sort numbers into sets? Can you give each set a name?

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.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

How many trains can you make which are the same length as Matt's, using rods that are identical?