Label this plum tree graph to make it totally magic!
A Sudoku with a twist.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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.
Solve the equations to identify the clue numbers in this Sudoku problem.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Use the clues about the shaded areas to help solve this sudoku
A pair of Sudoku puzzles that together lead to a complete 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.
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
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
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.
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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 arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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.
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.
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. . . .
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.
Two sudokus in one. Challenge yourself to make the necessary
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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.
Four small numbers give the clue to the contents of the four
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 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.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
A Sudoku with clues as ratios or fractions.
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?
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?
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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.