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

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

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...

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

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

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

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

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

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.

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?

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?

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?

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.

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?

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

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

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

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. . . .

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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

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

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

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?

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 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?"

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.

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

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

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

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. . . .

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

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

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

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

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

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?

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Can you work out how many lengths I swim each day?

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

Can you find any two-digit numbers that satisfy all of these statements?

How many noughts are at the end of these giant numbers?

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

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.