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

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

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

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

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?

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

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

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?

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?

Can you find the chosen number from the grid using the clues?

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?

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?

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?

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

Number problems at primary level that may require determination.

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

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

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.

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

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

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

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?

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 to work on with others.

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?

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.

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

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

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

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?

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.

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?

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

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?

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'.

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

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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?