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?
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.
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.
Here are some examples of 'cons', and see if you can figure out where the trick is.
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?
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. . . .
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. . . .
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.
This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with. . . .
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.
Who said that adding couldn't be fun?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
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.
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.
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
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?
Can you discover whether this is a fair game?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
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. . . .
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
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.
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Which hexagons tessellate?
A huge wheel is rolling past your window. What do you see?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.
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.
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Can you find different ways of creating paths using these paving slabs?
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?
When is it impossible to make number sandwiches?
Are these statements always true, sometimes true or never true?
Are these statements always true, sometimes true or never true?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?