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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
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.
The challenge is to find the values of the variables if you are to solve this Sudoku.
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?
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.
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 that uses transformations as supporting clues.
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
A Sudoku with a twist.
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 sudoku.
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.
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
This Sudoku combines all four arithmetic operations.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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. . . .
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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 total.
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?
Solve the equations to identify the clue numbers in this Sudoku 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?
Label this plum tree graph to make it totally magic!
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
This Sudoku requires you to do some working backwards before working forwards.
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?
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?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
A Sudoku with clues as ratios.
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.
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
A pair of Sudoku puzzles that together lead to a complete solution.
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four surrounding cells.
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?