Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Are these statements always true, sometimes true or never true?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

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?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.

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. . . .

Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.

Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation?

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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?

After some matches were played, most of the information in the table containing the results of the games was accidentally deleted. What was the score in each match played?

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

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

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?

Can you fit Ls together to make larger versions of themselves?

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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

What can you say about the angles on opposite vertices of any cyclic quadrilateral? Working on the building blocks will give you insights that may help you to explain what is special about them.

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Here are some examples of 'cons', and see if you can figure out where the trick is.

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .