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.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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

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.

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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?

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?

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....?

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?

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

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

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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.

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?

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

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

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

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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

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

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.

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

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

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?

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?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

In this matching game, you have to decide how long different events take.

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

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

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

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

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?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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!

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

An activity making various patterns with 2 x 1 rectangular tiles.

Can you draw a square in which the perimeter is numerically equal to the area?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?