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.
A Sudoku with a twist.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Solve the equations to identify the clue numbers in this Sudoku problem.
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
The challenge is to find the values of the variables if you are to
solve this Sudoku.
Label this plum tree graph to make it totally magic!
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 are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This Sudoku combines all four arithmetic operations.
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?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
A Sudoku with clues as ratios or fractions.
The clues for this Sudoku are the product of the numbers in adjacent squares.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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?
Use the clues about the shaded areas to help solve this sudoku
A pair of Sudoku puzzles that together lead to a complete solution.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Four small numbers give the clue to the contents of the four
A Sudoku that uses transformations as supporting clues.
Use the differences to find the solution to this Sudoku.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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.
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?
A Sudoku with clues given as sums of entries.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.