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?
This article for primary teachers suggests ways in which to help children become better at working systematically.
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.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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.
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.
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?
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.
Can you find all the different ways of lining up these Cuisenaire rods?
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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.
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?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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.
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
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?
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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....?
Can you find all the different triangles on these peg boards, and find their angles?
Can you fill in the empty boxes in the grid with the right shape and colour?