Who said that adding couldn't be fun?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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?
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.
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?
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
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. . . .
Replace each letter with a digit to make this addition correct.
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.
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...
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Are these statements always true, sometimes true or never true?
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?
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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?
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.
What are the missing numbers in the pyramids?
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 huge wheel is rolling past your window. What do you see?
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.
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.
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Choose any three by three square of dates on a calendar page...
Can you find all the 4-ball shuffles?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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. . . .
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 do. . . .
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?
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.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?
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?
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
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.
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.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.
Find the area of the annulus in terms of the length of the chord which is tangent to the inner 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.
Which hexagons tessellate?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?