Math Tricks

[Dave Venzke <dven -at- CLEO -dot- COM>]

On Tue, 23 Nov 1993, Doug Montalbano posted:
>This gambit reminds me that I have read the results of some research
>(mathematical, not reader-usability).

>You can go to any word in the dictionary by randomly opening by flipping
>forward and backward (that is,narrowing down the search area) not more than
>17 times.

>If 17 is the limit for one word in alphabetical order, what do you suppose
>the max number of times is for a page number?

and,

On Wed, 24 Nov 1993, Vicki Rosenzweig responded with:

>What a wonderful statistic. Does it depend on the size of the
>dictionary? (And how do you account for the OED, where you
>might have to "flip" between volumes?)

Sounds to me like Doug is referring to what is known as a binary search
algorithm:  a type of search in which an item is found by repeatedly
dividing an ordered list in two and searching the half that is known to
contain the item. With 17 tries, you can find any one page out of a total
of 131,072 (2 raised to the 17th power). Obviously (I love that word!),
this is *not* a random narrowing but a precise narrowing of the search area.

For those of you who'd like to put the idea to work (this is a
great cocktail party trick), you can *guess* a number between 1
and 100 in 7 or fewer tries; all you need to know is whether your
guess to too high or too low.

An example:

Find some sucker who likes to wager and have him or her pick any number
between 1 and 100 (actually this works with any number up to 128, but it's
easier to work with 100 in your head). Let's say the number picked is 90.

1: Is the number 50? (100/2)
   Too low.

2: Is the number 75? (50+(50/2))
   Too low.

3: Is the number 88? (75+(25/2))
   Too low.

4: Is the number 94? (88+(12/2))
   Too high.

5. Is the number 91? (94-(6/2))
   Too high.

6. Is the number 89? (91-(3/2))
   Too low.

7. Is the number 90? (89+(2/2))
   How did you do that?

What does this have to do with writing and page numbering? I don't know.
But it sure is a neat trick.

Dave Venzke                   | All opinions expressed here are solely my
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