Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Find out about Magic Squares in this article written for students. Why are they magic?!
An investigation that gives you the opportunity to make and justify
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?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Can you coach your rowing eight to win?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
This Sudoku, based on differences. Using the one clue number can you find the solution?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Given the products of adjacent cells, can you complete this Sudoku?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Four small numbers give the clue to the contents of the four