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?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
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.
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
A pair of Sudoku puzzles that together lead to a complete solution.
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.
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
A Sudoku that uses transformations as supporting clues.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
A Sudoku with clues as ratios.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
Use the differences to find the solution to 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
This Sudoku, based on differences. Using the one clue number can you find the solution?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
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 clue number in this sudoku is the product of the two numbers in adjacent cells.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four
Find out about Magic Squares in this article written for students. Why are they magic?!
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 of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Use the clues about the shaded areas to help solve this sudoku
Charlie and Abi 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 think?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A Sudoku with clues as ratios or fractions.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?
This Sudoku requires you to do some working backwards before working forwards.
Solve the equations to identify the clue numbers in this Sudoku problem.