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

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

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

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

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?

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?

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?

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

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?

Number problems at primary level that may require resilience.

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

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

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

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?

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?

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

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.

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

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

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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?

A collection of resources to support work on Factors and Multiples at Secondary level.

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

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?

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

If you have only four weights, where could you place them in order to balance this equaliser?

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?

Number problems at primary level to work on with others.

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

Given the products of diagonally opposite cells - can you complete this Sudoku?

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?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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?

Play this game and see if you can figure out the computer's chosen number.

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?

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?

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

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?"

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?

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.

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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

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.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Can you find any two-digit numbers that satisfy all of these statements?