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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
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?
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
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
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?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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 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.
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?
Label this plum tree graph to make it totally magic!
Solve the equations to identify the clue numbers in this Sudoku 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.
Two sudokus in one. Challenge yourself to make the necessary
A pair of Sudoku puzzles that together lead to a complete solution.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
A Sudoku that uses transformations as supporting clues.
My two digit number is special because adding the sum of its digits
to the product of its digits gives me my original number. What
could my number be?
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Four small numbers give the clue to the contents of the four
Use the differences to find the solution to this Sudoku.
This Sudoku combines all four arithmetic operations.
A Sudoku with clues as ratios.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
How many different symmetrical shapes can you make by shading triangles or squares?
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. . . .
Use the clues about the shaded areas to help solve this sudoku
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
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?