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?

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?

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

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?

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?

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

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

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

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 make square numbers by adding two prime numbers together?

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.

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

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

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?

Number problems at primary level that may require resilience.

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

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?

How many different rectangles can you make using this set of rods?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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?

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?

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?

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

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

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

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

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

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?

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 find the chosen number from the grid using the clues?

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

Can you complete this jigsaw of the 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?

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?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Number problems at primary level to work on with others.

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?

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

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

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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

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