Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Four small numbers give the clue to the contents of the four
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.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Use the differences to find the solution to this Sudoku.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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 game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
A Sudoku with clues as ratios.
A Sudoku with a twist.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
The challenge is to find the values of the variables if you are to
solve this Sudoku.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
A Sudoku with clues as ratios or fractions.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Can you use the information to find out which cards I have used?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
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.
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.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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 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.
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Two sudokus in one. Challenge yourself to make the necessary
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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. . . .
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.