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

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.

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

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.

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

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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.

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

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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?

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

How will you go about finding all the jigsaw pieces that have one peg and one hole?

What is the best way to shunt these carriages so that each train can continue its journey?

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

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....?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

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

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

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.

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

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

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?

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?

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

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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

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?

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

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

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

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.

Have a go at balancing this equation. Can you find different ways of doing it?

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