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.
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.
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.
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Try this matching game which will help you recognise different ways of saying the same time interval.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
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.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Find out what a "fault-free" rectangle is and try to make some of
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Can you find out in which order the children are standing in this
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Can you cover the camel with these pieces?
My coat has three buttons. How many ways can you find to do up all
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
What happens when you try and fit the triomino pieces into these
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?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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....?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Can you find all the different ways of lining up these Cuisenaire
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many trains can you make which are the same length as Matt's, using rods that are identical?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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 put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.