Solve the equations to identify the clue numbers in this Sudoku problem.
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
Label this plum tree graph to make it totally magic!
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
A Sudoku with a twist.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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 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?
Two sudokus in one. Challenge yourself to make the necessary
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?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This Sudoku, based on differences. Using the one clue number can you find the solution?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
Four small numbers give the clue to the contents of the four
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.
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
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 clues as ratios or fractions.
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. . . .
A Sudoku based on clues that give the differences between adjacent cells.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
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?
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?
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?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A pair of Sudoku puzzles that together lead to a complete solution.
A Sudoku with clues given as sums of entries.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?