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?

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

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

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

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

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

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?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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 find all the different ways of lining up these Cuisenaire rods?

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?

Find out about Magic Squares in this article written for students. Why are they magic?!

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

How many different triangles can you make on a circular pegboard that has nine pegs?

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

How many models can you find which obey these rules?

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.

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.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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....?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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.

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Find out what a "fault-free" rectangle is and try to make some of your own.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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

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.

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?

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

How many different rhythms can you make by putting two drums on the wheel?

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?

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?

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 triangles on these peg boards, and find their angles?

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

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?