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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.
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.
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