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.

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

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

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

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

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.

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

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?"

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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

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

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?

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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.

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.

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?

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

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

Can you work out what size grid you need to read our secret message?

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

A game that tests your understanding of remainders.

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

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.

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.

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

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

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

How many zeros are there at the end of the number which is the product of first hundred positive integers?

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

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

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?

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .