Find out about Magic Squares in this article written for students. Why are they magic?!
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.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Investigate the different ways you could split up these rooms so
that you have double the number.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many different journeys could you make if you were going to
visit four stations in this network? How about if there were five
stations? Can you predict the number of journeys for seven
This challenge is about finding the difference between numbers which have the same tens digit.
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?
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?
Find out what a "fault-free" rectangle is and try to make some of
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
This activity focuses on rounding to the nearest 10.
A Sudoku with clues given as sums of entries.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Can you make a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing it?
How many different triangles can you make on a circular pegboard that has nine pegs?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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.