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As the description of this repo says, this was an extra credit math problem for my class. It was not worth many points, so beware that the wording is not exact. It is hardly peer-reviewed, nor ready to be reviewed.
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This was a problem of the week (POTW) for my math class. I went way over the top with it. It was only worth 3 extra credit points, but I wanted a definitive answer to the question. I put in enough work for it to be worth keeping on my github.