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

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.

A Sudoku with clues given as sums of entries.

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

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.

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 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?

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

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

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?

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.

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

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?

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

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

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.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Find all the numbers that can be made by adding the dots on two dice.

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

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

This challenge is about finding the difference between numbers which have the same tens digit.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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 clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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?

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?

Can you use the information to find out which cards I have used?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

My coat has three buttons. How many ways can you find to do up all the buttons?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

How many different rhythms can you make by putting two drums on the wheel?

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