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?

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

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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?

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.

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?"

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

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

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

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Can you make lines of Cuisenaire rods that differ by 1?

Is there an efficient way to work out how many factors a large number has?

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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

Can you work out how many lengths I swim each day?

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

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

You'll need to know your number properties to win a game of Statement Snap...

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?