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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
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 Sudoku with clues given as sums of entries.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
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.
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.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
My coat has three buttons. How many ways can you find to do up all the buttons?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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.
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?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Can you find out in which order the children are standing in this line?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
How many models can you find which obey these rules?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
An investigation that gives you the opportunity to make and justify predictions.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
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?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.