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.
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.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Find out about Magic Squares in this article written for students. Why are they magic?!
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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?
A Sudoku with a twist.
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?
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?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Two sudokus in one. Challenge yourself to make the necessary
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
A Sudoku with clues as ratios or fractions.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku with clues as ratios.
A Sudoku that uses transformations as supporting clues.
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
A Sudoku based on clues that give the differences between adjacent cells.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
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?
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.
A Sudoku with clues given as sums of entries.
in how many ways can you place the numbers 1, 2, 3 … 9 in the
nine regions of the Olympic Emblem (5 overlapping circles) so that
the amount in each ring is the same?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Solve the equations to identify the clue numbers in this Sudoku problem.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
Imagine a stack of numbered cards with one on top. Discard the top,
put the next card to the bottom and repeat continuously. Can you
predict the last card?
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.