During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

The pages of my calendar have got mixed up. Can you sort them out?

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

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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?

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

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

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 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?

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

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

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?

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.

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

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

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 remover them. The winner is the last one to remove a counter. How you can make sure you win?

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....?

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.

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.

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.

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.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

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

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

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

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

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

Place the numbers 1 to 6 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?

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?

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

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

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?

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