Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

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?

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.

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.

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

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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?

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

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

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....?

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

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

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

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 arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

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

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

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

How many models can you find which obey these rules?

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

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?

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?

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?

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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

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?

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.