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.
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
A Sudoku with clues given as sums of entries.
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
Try this matching game which will help you recognise different ways of saying the same time interval.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
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.
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.
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.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Find out what a "fault-free" rectangle is and try to make some of your own.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
An investigation that gives you the opportunity to make and justify predictions.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
My coat has three buttons. How many ways can you find to do up all the buttons?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.