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.
A Sudoku with a twist.
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?
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.
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.
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?
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?
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.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Label this plum tree graph to make it totally magic!
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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 Sudoku that uses transformations as supporting clues.
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.
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.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with clues as ratios.
Four small numbers give the clue to the contents of the four
Two sudokus in one. Challenge yourself to make the necessary
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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 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.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Use the clues about the shaded areas to help solve 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
Use the differences to find the solution to this Sudoku.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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?
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. . . .
Find out about Magic Squares in this article written for students. Why are they magic?!
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
A Sudoku with clues as ratios or fractions.
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.
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.
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?