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?

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

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.

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.

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

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.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

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

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?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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

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

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

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?

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?

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?

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?

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

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

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

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

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....?

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

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.

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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