This article for primary teachers suggests ways in which to help children become better at working systematically.
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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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.
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.
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Find out what a "fault-free" rectangle is and try to make some of your own.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal 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?
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.
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 different triangles can you make on a circular pegboard that has nine pegs?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
A challenging activity focusing on finding all possible ways of stacking rods.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
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?
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?
How many different shapes can you make by putting four right- angled isosceles triangles together?
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?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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?
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....?
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?
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 clues to colour each square.
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Can you find all the different triangles on these peg boards, and find their angles?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?