### Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

### Watch the Clock

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?

### Take the Right Angle

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

# Six Places to Visit

##### Stage: 2 Challenge Level:

Thank you to children from Knaphill School who sent lots of solutions to this problem. Kevin described very carefully how to get to each of the places:

To the school:
At the first junction, turn clockwise $90^\circ$ go forward past the tall house.
When you see a turn, turn it by $45^\circ$ anti-clockwise.
Go forward until you see a little pink shop that's leaning over, there, you will find the next junction, turn $45^\circ$ anti-clockwise then go forward. You will see a blue church.
Go straight past it then there will be a third junction, turn clockwise $90^\circ$.
Go forward till you see the fourth junction! At this junction, you turn clockwise and $90^\circ$.
Go forward and soon you will see a white house with trees around it, ignore it.
Carry on going forward until you see a turn, turn it by turning it clockwise $45^\circ$.
Start going forward again, there will be another $45^\circ$ turn clockwise soon after, then you will come to the school.

To the red house:
Go forward until you see a turn, turn it by turning $90^\circ$ anti-clockwise.
Go forward and you're there!

To the tall house:
Go forward until you see the first junction, turn $90^\circ$ clockwise go forward and then you'll be there. Easy-Peasy.

To the pink shop that's leaning over:
Go forward until you see the first junction, turn $90^\circ$ clockwise
Go forward again, past the tall house.
Then you'll see the second junction, turn $45^\circ$ anti-clockwise and go forward. That's where the pink shop that's leaning over is.

To the blue church:
Go forward until you see the first junction, turn $90^\circ$ clockwise
Go forward again, past the tall house.
You will see a $45^\circ$turn, turn anti-clockwise.
Go forward again, then comes the 2nd junction, turn $45^\circ$ anti-clockwise, go forward and soon comes the blue church.

To the house with trees:
Go forward till you get to the first junction, turn clockwise by $90^\circ$
Go forward past the tall house, then the $45^\circ$ turn anti-clockwise
Go forward till the second junction, turn $90^\circ$ clockwise
Then you will come to a $45^\circ$ turn anti-clockwise, past the school
Then you'll come to another $45^\circ$ anti-clockwise turn
After that, go forward till another $45^\circ$ anti-clockwise turn!
Go forward another little bit then you'll be at the house with trees!

Jack from Eastwood Primary School described visiting all the places in one journey. This is what he wrote:

Starting at the yellow house, you move forward, passing the T junction on your right until you reach the end of the road. There, turn left $90^\circ$, move forward until you reach the red brick house with the blue roof. Enter the house.
When leaving the house, turn left and follow the road until it turns right $90^\circ$, continue forward and take the first turning on the left. Follow the road until you reach the tall house, and enter.
Come out of the house and turn left. Follow the road which turns left at a $45^\circ$ angle. At the Y junction, you will see a small white house on your left, enter.
When exiting the house turn left and follow the road forward until you see a blue church on your right-hand side. Visit the church.
Exit the church and continue in the same direction as before. When reaching the T junction, turn right. Continue forward and take the next turning on your right which is at a $90^\circ$ angle. Go forward until you reach a small cottage on your right, enter for some tea.
Come out of the cottage and turn right, move forward along the road where it will bend at a $45^\circ$ angle to the right, continue forward where the road will bend again to the right at a $45^\circ$ angle. Move forward, there will be a large school on your right-hand side, enter the school and go to Mr Leggett's maths lesson.

Well done, Jack, that's a very efficient way of visiting each place in turn.

Thank you to everyone else who sent us their detailed description. Unfortunately there isn't space to publish them all!