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.
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?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
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 ...?
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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?
How many models can you find which obey these rules?
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?
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
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?
Can you find out in which order the children are standing in this line?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
My coat has three buttons. How many ways can you find to do up all the buttons?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
An investigation that gives you the opportunity to make and justify predictions.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Find all the numbers that can be made by adding the dots on two dice.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?