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Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to. . . .
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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.
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?
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.
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...
Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?
Replace each letter with a digit to make this addition 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. . . .
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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. . . .
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. . . .
Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?
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.
Here are some examples of 'cons', and see if you can figure out where the trick is.
Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.
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?
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. . . .
What are the missing numbers in the pyramids?
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
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.
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?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Which set of numbers that add to 10 have the largest product?
Can you find all the 4-ball shuffles?
Can you fit Ls together to make larger versions of themselves?
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?
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?
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?
From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How. . . .
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?
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
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.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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.
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.
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.
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.
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.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?
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.
Is it true that any convex hexagon will tessellate if it has a pair of opposite sides that are equal, and three adjacent angles that add up to 360 degrees?