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 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.

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

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

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.

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?

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

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

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

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

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?

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?

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

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.

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

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

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

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.

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

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

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.

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....?

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

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

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.

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. . . .

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

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

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

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?

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?

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?

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

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.

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

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

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

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?

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.