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?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
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. . . .
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
A Sudoku with a twist.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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....?
A Sudoku with clues as ratios.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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 challenge extends the Plants investigation so now four or more children are involved.
What could the half time scores have been in these Olympic hockey matches?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Four small numbers give the clue to the contents of the four
A Sudoku with clues as ratios or fractions.
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This Sudoku combines all four arithmetic operations.
Can you find all the different triangles on these peg boards, and
find their angles?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Find out what a "fault-free" rectangle is and try to make some of
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
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 Sudoku, based on differences. Using the one clue number can you find the solution?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Two sudokus in one. Challenge yourself to make the necessary
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
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?
Can you find all the different ways of lining up these Cuisenaire