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.

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

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.

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

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?

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

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

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

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?

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.

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 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 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.

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?

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

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

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

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.

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

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

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?

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?

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?

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

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

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?

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

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?

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?

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?

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

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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