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. . . .

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

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

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

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.

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?"

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?

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

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.

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

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

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

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

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

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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

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

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.

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?

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...

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

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

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

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?

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

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

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?

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

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

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

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...

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

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.

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?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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

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

Find the highest power of 11 that will divide into 1000! exactly.

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

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

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?

Here is a chance to create some Celtic knots and explore the mathematics behind them.

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