An investigation that gives you the opportunity to make and justify
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?!
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Can you coach your rowing eight to win?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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 put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
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 focuses on finding the sum and difference of pairs of two-digit numbers.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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!
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Four small numbers give the clue to the contents of the four