Which way are you facing?

In your book, Maths Mela (Chapter 3), children play a turning game. The teacher tells them how to turn, and they must say which direction they face at the end. The four directions are North, East, South and West. On the book's compass, North is at the top, East on the right, South at the bottom and West on the left.

Turning clockwise (the way clock hands move), the directions come in this order: North, East, South, West, and then back to North. Each step from one direction to the next is a quarter turn, which is one right angle. Turning anti-clockwise, they come in the opposite order: North, West, South, East, and back to North.

Start facing North and turn two right angles clockwise: North to East is one, East to South is two. You face South, the opposite way. Two right angles make a half turn, and a half turn, clockwise or anti-clockwise, always makes you face the opposite way. Four right angles make a full turn, so starting facing East and turning four right angles anti-clockwise, you face East again.

What about five right angles clockwise from North? Four of them bring you back to North, and one more takes you to East. So you face East.

Then we meet Padma. She is standing in a street, facing the toy shop, 'Toy Dukan'. There is a bookstore on her left, and an ice-cream cart right behind her. If she takes a half turn clockwise, she faces the opposite way, so she faces the ice-cream cart. Another way to face the cart is a half turn anti-clockwise: a half turn either way ends up facing the same way.