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?!
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 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.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
A Sudoku with clues given as sums of entries.
Find all the numbers that can be made by adding the dots on two dice.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
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.
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.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
My coat has three buttons. How many ways can you find to do up all the buttons?
A challenging activity focusing on finding all possible ways of stacking rods.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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.
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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
How many models can you find which obey these rules?
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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
This challenge extends the Plants investigation so now four or more children are involved.
Can you fill in the empty boxes in the grid with the right shape and colour?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
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?
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.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
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?
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?
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?
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?