Investigate circuits and record your findings in this simple introduction to truth tables and logic.

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.

Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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.

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.

A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.

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?

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

An article which gives an account of some properties of magic squares.

Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?

If you think that mathematical proof is really clearcut and universal then you should read this article.

Keep constructing triangles in the incircle of the previous triangle. What happens?

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

The final of five articles which containe the proof of why the sequence introduced in article IV either reaches the fixed point 0 or the sequence enters a repeating cycle of four values.

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.

Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

Can you rearrange the cards to make a series of correct mathematical statements?

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?

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

This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning.

Can you make sense of the three methods to work out the area of the kite in the square?

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

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

Can you make sense of these three proofs of Pythagoras' Theorem?

What fractions can you divide the diagonal of a square into by simple folding?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.