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?"

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

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

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

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 that tests your understanding of remainders.

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.

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?

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

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

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 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?

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

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.

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

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

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. . . .

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" .

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 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 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?

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

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

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?

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

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

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

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.

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?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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?

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.

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

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?

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

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

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

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

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

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

Can you find a way to identify times tables after they have been shifted up?

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

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.

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?

What is the smallest number of answers you need to reveal in order to work out the missing headers?