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?
A pair of Sudoku puzzles that together lead to a complete solution.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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.
Four small numbers give the clue to the contents of the four
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This Sudoku combines all four arithmetic operations.
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.
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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.
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?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
A Sudoku that uses transformations as supporting clues.
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.
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.
Use the differences to find the solution to this 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. . . .
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
You need to find the values of the stars before you can apply normal Sudoku rules.
Two sudokus in one. Challenge yourself to make the necessary
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
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.
Given the products of adjacent cells, can you complete this Sudoku?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Solve the equations to identify the clue numbers in this Sudoku problem.
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?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one