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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
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.
Find out what a "fault-free" rectangle is and try to make some of your own.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal 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.
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?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
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.
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?
How many different rhythms can you make by putting two drums on the wheel?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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....?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Try out the lottery that is played in a far-away land. What is the chance of winning?
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.
My coat has three buttons. How many ways can you find to do up all the buttons?
Can you find all the different triangles on these peg boards, and find their angles?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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?
This challenge extends the Plants investigation so now four or more children are involved.
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.
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?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.