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Guess Stars is a puzzle in Professor Layton and the Miracle Mask.

Puzzle

The bartender places five bottle caps on the bar, with the star logos facing up. She closes her eyes and starts turning caps over at random, counting every turn.

Once she reaches 25, she suddenly slams her hand onto the bar, covers up one of the caps, and asks you, "Is the logo on this cap facing up or down?"

With the situation shown in the diagram above, can you answer her question?

Hints




Click a Tab to reveal the Hint.

The best way to solve this puzzle is to try it out. Find something nearby that can stand for the caps, and give it a try.

Once you realize a particular rule, you won't need to flip the caps over 25 times to work out the answer.

All the caps started facing up. If you flip one over, then four are facing up and one is facing down, right?

Now flip another over and you'll have three facing up and two facing down.

If you flip another, that's two facing up and three facing down.

Notice any pattern here?

Think carefully about the relationship between the number of times a cap has been flipped and the number of caps still facing up.

When the number of flips is even, the number of caps facing up is odd. If you keep this in mind, you won't need to flip them 25 times to solve the puzzle.

When the number of flips is odd, the number of caps facing up must be even.

Notice 25 flips is an odd number, and two of the visible caps are facing up, which can only mean one thing.


Solution

Incorrect

Too bad.

Do you notice anything as you keep flipping caps over and over?

Correct

Correct!

The cap is facing down.

Flip the caps an odd number of times and the number of caps facing up will be even, and vice versa.

Since 25 is an odd number, there can only be 2 caps facing up, so the covered one must be facing down.

A big thanks to http://www.youtube.com/user/LaytonKyouju

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