This week's puzzle is a practical one; you can solve it with pen and paper, but it's a lot more fun to try this real-world phenomenon for yourself.
Sunday Puzzle #14: How Much Of Yourself Can You See In A Mirror?
Imagine you are standing before a small wall-mirror. This is no funhouse mirror; it is perfectly flat, and mounted flush with the vertical wall on which it hangs. How much of yourself do you see in the mirror? What if you take a few steps backward, away from the mirror? Can you see more of yourself? Less of yourself? How big of a mirror would you need to see your entire head reflected back at you, at a given distance? How big of a mirror would you need to see your entire body reflected back at you? (Bear in mind: The mirror depicted in the art at the top of this post has not been drawn to scale.)
We'll be back next week with the solution – and a new puzzle! Got a great brainteaser, original or otherwise, that you'd like to see featured? E-mail me with your recommendations. (Be sure to include "Sunday Puzzle" in the subject line.)
UPDATE: The solution to this puzzle has been posted here.
Art by Tara Jacoby
SOLUTION To Sunday Puzzle #13: Mathematical Poetry
Last week, I showed you the following mathematical equation. Said equation is already balanced; the quantity on both sides of the equals sign is 81:
What's interesting about this equation, however, isn't that it's balanced, but what it sounds like when read aloud. This expression, it turns out, is a mathematical limerick. When read aloud, it matches the rhyme scheme of a five-line limerick. (AABBA). But there's a bit of a twist.
If you read this equation as written, speaking the words "twelve," "one-hundred forty-four," and "twenty" aloud, you run into some funny issues matching the classical limerick rhyme scheme with the stress and meter typical of the form. The crux of the puzzle, then, is figuring out a different way to speak the numerals 12, 144, and 20 aloud. As many of you correctly noted in the comments, these can also be expressed as a dozen, a gross, and a score, which gives us:
A dozen, a gross, and a scorePlus three times the square root of fourDivided by sevenPlus five times elevenIs nine squared and not a bit more.
This particular mathematical limerick was created by British wordplay expert Leigh Mercer (perhaps best known for writing the palindrome "A man, a plan, a canal — Panama!"), and originally appeared in a 1980 issue of Word Ways. Find more mathematical limericks here.