Answers

1. The equation is a straightforward substitution encryption. Hint: To make the code easier to crack, write it out in this form:  WWWDOT -GOOGLE --------------------  DOTCOM Then, it’s a matter of finding the correct digits to substitute for the letters. This can be done through the brute force method of trial-and-error, but a more Googley way to solve it would be to write a computer program. See this MathWorld page for some suggestions. Hopefully you’ll end up with:  777589 -188103 --------------------  589486 * As the question noted, the M and E are interchangeable. If you make M=3 and E=6, the answer would be 589483. 2. Since there are no right or wrong answers in poetry, we offer no suggestions beyond a reminder to follow the haiku syllable rule (5 – 7 – 5). But we are interested in your creations. Have a poem that you’d like to share? Email GLAT (at) thegooglestory.com 3. This is a deceptive puzzler. Hint: Try reading each digit aloud from left to right. One One One Two One One Two One One One One One Two Two One Still stumped? Here’s a second hint / spoiler: One One One Two One One Two, One One One One, One Two, Two One The Solution: Each line describes the numbers in the line above it. So the next line would read: 312211 aka Three Ones, Two Twos, One One. 4. Thou dost answer as thou please. 5. There are no shortage of opinions on this. The folks at MathWorld have an amusing take. 6. D. Or, if you can, E. 7. People are most familiar with Google’s mantras A) "I’m feeling lucky" and B) "Don’t be evil," but the answer is actually E) All of the above. 8. The question "What is an icosahedron?" would be enough of a challenge for most of us, nevermind the calculations about how many ways to color it. As it happens, icosahedron is the technical term for a 20-sided solid, though the question doesn’t specify whether the icosahedron is regular (symmetric) or irregular (having sides of varying shape and size). If we’re not talking about a regular icosahedron, the answer is: 3^20 (three to the power of 20) In the case of a regular icosahedron, you’d have to take into account rotational equivalency and bisymmetry, reducing the number of combinations, for an answer of: (3^20)/20 (three to the power of 20, all divided by 20) The second part of the question -- what colors to choose -- is of course a matter of personal preference, but Googlers will expect you to have a good reason for your choices. David opts for red, white and black, Maryland Terrapins colors, while Mark, a lifelong Philadelphia Flyers fan, picks orange, black, and white. 9. How to improve upon emptiness? Some suggestions:      -- Write out beautiful math equations (see #12)      -- Paste a photograph of a loved one.      -- Fill it with Google text ads      -- Draw a map to buried treasure. 10. We’re still working on this one. If you’re interested, see a thorough examination of the problem at MathWorld and Cruftbox.com 11. Surf? Surf. 12. Ah, beauty. We won’t attempt to judge the merit of the many possible answers to this question, but rather leave it to the eye of the beholder. Our own nominee is the equation that yields the magical number phi (1.618...), the “golden ratio” that is found abundantly in nature, in Man, sunflowers, seashells, as well as the pyramids, the Parthenon, Renaissance art, even the DaVinci Code. Its beauty has stood the test of time. 13. D. 14. Sergey Brin has one suggestion that appears on the last page of The Google Story. It may take some time yet, but it is inevitable. 15. B 16. This problem calls for finding the Isoperimetric point. A Cornell student, Elliott Back, posted this answer on his Web site, which looks right to us. Draw a circle around C of radius (a+b-c)/2. This makes it easy to draw circles around A and B which are tangent to C. You have three small circles--now draw a final circle outside and tangent to circles A, B, C. The center of this circle is P. This is also known as Apollonius' problem. 17. 199981. This requires a computer program to solve, or a lot of patience. 18. If you’re interested in cool hacks, Tara Calishain’s book Google Hacks is a good place to turn. We also like the many cool and useful things being done with Google Maps. See the Google Maps Mania blog for a good collection. 19. The first half of the question is a fancy way of stating the binomial coefficient: (n, k) = (n, n-k) An identity which solves the problem is (n-1, k-1) + (n-1, k) = (n, k). Or, in words, "I pick k-1, you pick k." Thanks, Elliott. 20. Hint: Write out the numbers, one below another. ten nine sixty ninety seventy sixty-six The answer: Each number, when spelled out, is the largest for that given word size. Ten is the largest number with three letters; nine the largest with four. Thus, the next line in the series is the largest number with nine letters. That number is ninety-six, so the correct answer is A. 21. We’d love to know your ideas as we continue to cover Google and work on future editions of The Google Story.