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?

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 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?

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

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

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

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?

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

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?

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?

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?

Number problems at primary level that may require resilience.

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?

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

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?

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

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

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.

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?

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

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

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?

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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?

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

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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

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?

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?

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.

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

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!

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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?

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

Given the products of adjacent cells, can you complete this Sudoku?

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

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

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?

Can you explain the strategy for winning this game with any target?

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

"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 ...?

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

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

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?"

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?