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.

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

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

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

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

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?"

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.

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

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. . . .

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

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

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. . . .

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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

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

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

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.

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 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?

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

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?

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

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

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.

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" .

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

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

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

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

Can you find what the last two digits of the number $4^{1999}$ are?

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

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 the number which has 8 divisors, such that the product of the divisors is 331776.

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.

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

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

Have you seen this way of doing multiplication ?

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

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

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?

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

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

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

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.

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...

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

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?