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?
Find out about Magic Squares in this article written for students. Why are they magic?!
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Label this plum tree graph to make it totally magic!
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
A pair of Sudoku puzzles that together lead to a complete 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?
Four small numbers give the clue to the contents of the four
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Use the differences to find the solution to this 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.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
You need to find the values of the stars before you can apply normal Sudoku rules.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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 diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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?
A Sudoku with clues as ratios.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
A Sudoku that uses transformations as supporting clues.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Two sudokus in one. Challenge yourself to make the necessary
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?
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?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
This Sudoku combines all four arithmetic operations.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
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 Sudoku with a twist.