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?

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

A Sudoku with clues given as sums of entries.

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?

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 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?

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.

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

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

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?

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.

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

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?

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....?

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

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

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

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.

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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?

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.

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?

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

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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

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

What could the half time scores have been in these Olympic hockey matches?

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

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?

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

How many models can you find which obey these rules?

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

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal 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 work out how to balance this equaliser? You can put more than one weight on a hook.

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

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?

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

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

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?