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.
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.
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?
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.
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?
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. . . .
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
Can you use the information to find out which cards I have used?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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?
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 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?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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.
Follow the clues to find the mystery number.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Find out what a "fault-free" rectangle is and try to make some of
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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?
Can you find all the different ways of lining up these Cuisenaire
An investigation that gives you the opportunity to make and justify
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
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?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?