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Ride Rotation is a puzzle in Professor Layton and the Miracle Mask.

Puzzle

A girl tries a spinning teacup ride, beloved at amusement parks across the world.

There are four saucers on the ride's base and four cups on each saucer. The base, saucers, and cups each take 20 seconds to make one complete clockwise rotation.

If the girl in the picture is facing east now, which way will she be facing after the cup has spun for 15 seconds?

Hints

Click a Tab to reveal the Hint.

You know that it takes 20 seconds to complete one rotation. That means in 15 seconds, you'll get a three-quarter rotation. So three quarter rotations each for the base, saucer, and cup gives you...

That's a bit confusing, isn't it? Isn't there an easier way?

The girl is sitting in the cup, so you'll need to add up all the rotations of the base, saucer, and cup. In that case, you can express the problem in simple math.

Each makes one three-quarter rotation, and one rotation is 360 degrees, so it's 270 degrees each.

Calculate the total rotations of the base, cup, and saucer. That's 810 degrees (270 degrees times 3.)

A full rotation is 360 degrees, and two full rotations will put you at 720 degrees. You can then go an additional 90 degrees from there.

Where would that leave the girl facing?

You'll end up with two full rotations and a 90-degree rotation. That means you only need to think about the 90-degree rotation.

In other words: the direction she'll be facing is just a one-quarter rotation from her starting position. Where is that?