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1.8: Summary and Further Problems

  • Page ID
    27636
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    The main lesson that you should take away is courage: No problem is too difficult. We just use divide-and-conquer reasoning to dissolve difficult problems into smaller pieces. (For extensive practice, see the varied examples in the Guesstimation books [47 and 48].) This tool is a universal solvent for problems social and scientific.

    Exercise \(\PageIndex{1}\): Per-capita land area

    Estimate the land area per person for the world, for your home country, and for your home state or province

    Exercise \(\PageIndex{2}\): Estimate the mass of the Earth

    Then look it up (p. xvii) to check your estimate.

    Exercise \(\PageIndex{3}\): Billion

    How long would it take to count to a billion (109)?

    Exercise \(\PageIndex{4}\): Sweating

    Estimate how much water you need to drink to replace water lost to evaporation, if you ride a bicycle vigorously for 1 hour. Represent your estimate as a divide-and-conquer tree. Hint: Humans are only about 25 percent efficient in generating mechanical work.

    Exercise \(\PageIndex{5}\): Pencil line

    How long a line can you write with a pencil?

    Exercise \(\PageIndex{6}\): Pine needles

    Estimate the number of needles on a pine tree.

    Exercise \(\PageIndex{7}\): Hairs

    How many hairs are on your head?


    This page titled 1.8: Summary and Further Problems is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Sanjoy Mahajan (MIT OpenCourseWare) .

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