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

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.

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

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

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

Substitution and Transposition all in one! How fiendish can these codes get?

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?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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.

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

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" .

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?

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.

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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?

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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?

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...

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?

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. . . .

Explore the relationship between simple linear functions and their graphs.

A game that tests your understanding of remainders.

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.

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?

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

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.

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

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

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

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

Have you seen this way of doing multiplication ?