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Diamond in the Flag is a puzzle in Professor Layton and the Curious Village.

Puzzle

Below is a diagram of a flag.

From the measurements shown on the diagram, can you calculate what fraction of the flag's total area is represented by the diamond in the middle? Your answer will be the denominator for a fraction in 1/X form.

US Version

Don't complicate things by bringing trigonometry into the mix. The solution is simple enough to work out in your head.

UK Version

Hints

Click a Tab to reveal the Hint.

Help yourself out by dividing up the flag.

First, split the flag into four equally sized rectangles by drawing a vertical line and a horizontal line through the middle of the flag. This will divide the diamond into quarters as well.

Examine one of the flag's new quarters.

These smaller rectangles can actually be broken down into fourths again. Be careful when calculating the length for each side. Is each small rectangle really 30 by 20 inches?

When you divide the small rectangle into fourths, you will end up including a portion of the diamon in one of the smallest rectangles.

What fraction of the rectangle's area does that slice of the diamond represent?

Figure that out and you're a step away from the solution.

Solution

Incorrect

Not quite.

Remember, don't bother with complex math to find a solution. Look closely at the diagram.

Correct

Nicely done!

US Version

The measurements on each area of the diagram are the key to this puzzle. If you draw a line or two to supplement the diagram's information, it's easy to see that the diamond represents one-eighth of the flag's area.

UK Version

The measurements on each area of the diagram are the key to the puzzle. If you divide a quarter of the flag into four parts as shown, it's easy to see that half the flag's area. That makes the whole diamond one-eighth of the flag's area in total.

A big thanks to http://professorlaytonwalkthrough.blogspot.com

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