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 given as sums of entries.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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.
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
What could the half time scores have been in these Olympic hockey matches?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you find all the different triangles on these peg boards, and
find their angles?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Find out what a "fault-free" rectangle is and try to make some of
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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....?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you find all the different ways of lining up these Cuisenaire
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.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
How many trains can you make which are the same length as Matt's, using rods that are identical?