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.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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.
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Follow the clues to find the mystery number.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
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?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you use the information to find out which cards I have used?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Find out about Magic Squares in this article written for students. Why are they magic?!
A Sudoku with clues given as sums of entries.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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. . . .
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
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?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
An investigation that gives you the opportunity to make and justify
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?