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?
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?
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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.
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku with a twist.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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 based on clues that give the differences between adjacent cells.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with clues as ratios.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Given the products of diagonally opposite cells - can you complete this Sudoku?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A Sudoku that uses transformations as supporting clues.
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?
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?
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?
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.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
A Sudoku with clues given as sums of entries.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
You have twelve weights, one of which is different from the rest.
Using just 3 weighings, can you identify which weight is the odd
one out, and whether it is heavier or lighter than the rest?
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A Sudoku with clues as ratios or fractions.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Take three whole numbers. The differences between them give you
three new numbers. Find the differences between the new numbers and
keep repeating this. What happens?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Can you coach your rowing eight to win?