How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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.
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?
Find out what a "fault-free" rectangle is and try to make some of
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
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.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you find all the different triangles on these peg boards, and
find their angles?
This Sudoku, based on differences. Using the one clue number can you find the solution?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Can you find all the different ways of lining up these Cuisenaire
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
A Sudoku with a twist.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
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 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
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
A Sudoku that uses transformations as supporting clues.
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
You need to find the values of the stars before you can apply normal Sudoku rules.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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. . . .
How many different triangles can you make on a circular pegboard that has nine pegs?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.