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Mike has always been terrible at math. He's asked to "multiply a certain number by 9, then add 7," but instead he multiplies by 7 and adds 9.
He soon notices his error and starts to panic. When he tries to do the problem correctly, he ends up getting the same answer as when he made the mistake the first time. It's all an accident, but what is that "certain number," the one marked with a question mark below?
The number is one.
If you do the math, it all works out.
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A big thanks to http://professorlayton2walkthrough.blogspot.com