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

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?

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.

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?

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?

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

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

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

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

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

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?

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?

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

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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 complete this jigsaw of the multiplication square?

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 find the chosen number from the grid using the clues?

This package will help introduce children to, and encourage a deep exploration of, multiples.

Can you find any perfect numbers? Read this article to find out more...

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

Number problems at primary level to work on with others.

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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?

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

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

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 that may require determination.

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

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?

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?

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?

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

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?

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

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?

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

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

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?

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

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?

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?