A Sudoku with clues given as sums of entries.

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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?

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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.

What happens when you try and fit the triomino pieces into these two grids?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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.

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

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?

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.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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.

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous 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.

Can you find all the different triangles on these peg boards, and find their angles?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

This challenge extends the Plants investigation so now four or more children are involved.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

How many models can you find which obey these rules?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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 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.

This dice train has been made using specific rules. How many different trains can you make?

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.

In this matching game, you have to decide how long different events take.

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

A challenging activity focusing on finding all possible ways of stacking rods.

Try this matching game which will help you recognise different ways of saying the same time interval.

Try out the lottery that is played in a far-away land. What is the chance of winning?

Find all the numbers that can be made by adding the dots on two dice.