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?
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.
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
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.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Find out about Magic Squares in this article written for students. Why are they magic?!
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve 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.
Given the products of adjacent cells, can you complete this Sudoku?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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 puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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 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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Sudoku with clues as ratios.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
A Sudoku that uses transformations as supporting clues.
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?
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?
Use the clues about the shaded areas to help solve this sudoku
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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?
Two sudokus in one. Challenge yourself to make the necessary
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.
Four small numbers give the clue to the contents of the four
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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. . . .
This Sudoku combines all four arithmetic operations.
A pair of Sudoku puzzles that together lead to a complete solution.
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
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind