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?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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 with clues as ratios or fractions.
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
This Sudoku combines all four arithmetic operations.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
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?
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Sudoku with clues as ratios.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Four small numbers give the clue to the contents of the four
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
A Sudoku with a twist.
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 pair of Sudoku puzzles that together lead to a complete solution.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
A Sudoku that uses transformations as supporting clues.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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 need to find the values of the stars before you can apply normal Sudoku rules.
Two sudokus in one. Challenge yourself to make the necessary
This Sudoku, based on differences. Using the one clue number can you find the solution?
Use the clues about the shaded areas to help solve this sudoku
Solve the equations to identify the clue numbers in this Sudoku problem.
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.
This Sudoku requires you to do some working backwards before working forwards.
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 challenge is to find the values of the variables if you are to
solve this Sudoku.
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?
Label this plum tree graph to make it totally magic!
A Sudoku with clues given as sums of entries.
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?
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?