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

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

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?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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?

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?

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

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?

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

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

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

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

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?

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.

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

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

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

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

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 make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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

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

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

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

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

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

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.

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....?

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

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

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

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?

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?

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

A challenging activity focusing on finding all possible ways of stacking rods.

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?

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?

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

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Try this matching game which will help you recognise different ways of saying the same time interval.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.