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 numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
A Sudoku with a twist.
Solve the equations to identify the clue numbers in this Sudoku problem.
You need to find the values of the stars before you can apply normal Sudoku rules.
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
Label this plum tree graph to make it totally magic!
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.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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?
A Sudoku with clues as ratios or fractions.
This Sudoku combines all four arithmetic operations.
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Use the clues about the shaded areas to help solve this sudoku
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?
A Sudoku with clues as ratios.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
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?
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?
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 pair of Sudoku puzzles that together lead to a complete solution.
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.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Four small numbers give the clue to the contents of the four
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 differences to find the solution to this Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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
Find out about Magic Squares in this article written for students. Why are they magic?!
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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.
This Sudoku requires you to do some working backwards before working forwards.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A Sudoku with clues given as sums of entries.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.