This article for primary teachers suggests ways in which to help children become better at working systematically.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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?
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?
Try this matching game which will help you recognise different ways of saying the same time interval.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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.
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.
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?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
This challenge extends the Plants investigation so now four or more children are involved.
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?
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.
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....?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Can you find out in which order the children are standing in this line?
Find out what a "fault-free" rectangle is and try to make some of your own.
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
A challenging activity focusing on finding all possible ways of stacking rods.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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?
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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 trains can you make which are the same length as Matt's, using rods that are identical?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Can you find all the different ways of lining up these Cuisenaire rods?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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.
Can you find all the different triangles on these peg boards, and find their angles?
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.
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?
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.