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Let's say you took a square piece of paper and cut off the corners to make the largest possible circle. But then you realize you needed a square piece instead and cut off the curves to make the largest possible square. How many times bigger was the original square than the one you have now.
You got it!
The original square was twice as big. It's very easy to see when you draw a diagram.
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A big thanks to http://professorlayton2walkthrough.blogspot.com