in how many ways can you place the numbers 1, 2, 3 … 9 in the
nine regions of the Olympic Emblem (5 overlapping circles) so that
the amount in each ring is the same?
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
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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 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 Sudoku with a twist.
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
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.
Charlie and Lynne put a counter on 42. They wondered if they could
visit all the other numbers on their 1-100 board, moving the
counter using just these two operations: x2 and -5. What do you
This Sudoku, based on differences. Using the one clue number can you find the solution?
A Sudoku with clues as ratios.
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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.
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?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku that uses transformations as supporting clues.
Find out about Magic Squares in this article written for students. Why are they magic?!
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
A Sudoku with clues as ratios or fractions.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
The clues for this Sudoku are the product of the numbers in adjacent squares.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
A Sudoku based on clues that give the differences between adjacent cells.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
A Sudoku with clues given as sums of entries.
Label this plum tree graph to make it totally magic!
Two sudokus in one. Challenge yourself to make the necessary
A pair of Sudoku puzzles that together lead to a complete solution.
Solve the equations to identify the clue numbers in this Sudoku problem.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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
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.
This Sudoku requires you to do some working backwards before working forwards.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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. . . .