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?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
A Sudoku with clues as ratios.
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?
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
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?
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.
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
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
A Sudoku with a twist.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
A Sudoku with clues as ratios or fractions.
A Sudoku that uses transformations as supporting clues.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Find out what a "fault-free" rectangle is and try to make some of
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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.
This Sudoku combines all four arithmetic operations.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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?
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?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?