in reply to 2, 2, 2, 3, 7, 22, 83, ...

How appropriate. ;-)

Hint and spoiler:

The series in question is described by the following problem:

Given an unlimited supply of bananas, how far can a camel walk into the desert if it can carry only one banana at a time and if it eats one banana per mile?

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Replies are listed 'Best First'.
Re^2: 2, 2, 2, 3, 7, 22, 83, ...
by jbrugger (Parson) on Feb 06, 2006 at 13:45 UTC
    Wow, now that you spoiled me, (and i guessed wrong of course) i admit i never saw
    <Reveal this spoiler or all in this thread>
    this coming!
    Thanks for the enlightment, and making me feel a complete idiot :)

    "We all agree on the necessity of compromise. We just can't agree on when it's necessary to compromise." - Larry Wall.
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Re^2: 2, 2, 2, 3, 7, 22, 83, ...
by davido (Cardinal) on Feb 06, 2006 at 16:53 UTC
[reply]

      The second link is better in one respect anyway; it notes that the equation provides an approximation.

      It takes 0 (not 2) bananas to go 0 miles into the desert. It takes 1 banana (not 2) to go 1 mile into the desert. It takes 2 bananas to go 2 miles into the desert. I suspect it takes 6 (not 3 nor 7) bananas to go 3 miles into the desert, but don't ask me how to accomplish it...

      Which means we may not know exactly how many bananas it takes to reach the next milestone. It is approximately 326 but, in my 20-second perusal of the links provided, I don't see an exact answer.

      Update: You can get 3 miles on 6 bananas: 

      At
  0: eat 1, carry 1 (2 used)
1/2: drop 1 (1/2 in stomach, 1@1/2)
  0: eat 1, carry 1 (4 used)
1/2: drop 1 (1/2 in stomach, 2@1/2)
  0: eat 1, carry 1 (6 used)
3/4: drop 1 (1/4 in stomach, 2@1/2, 1@3/4)
1/2: eat 1, carry 1 (0@1/2, 1@3/4)
  1: drop 1 (1/2 in stomach, 1@3/4, 1@1)
3/4: carry 1 (1/4 in stomach, 0@3/4, 1@1)
  1: eat 1 (0@1, still carrying 1)
  2: eat 1 (carrying 0)
  3: hope the report of "bananas 3 miles in" are true

      [download]

      Update2: And you can get 4 miles w/ 22 bananas: 

      At
  0: eat 1, carry 1 (2 used)
1/2: drop 1 (1/2 in stomach, 1@1/2)
  0: repeat above 9 more times (20 used, 10@1/2)
  0: eat 1, carry 1 (22 used)
3/4: drop 1 (1/4 in stomach, 10@1/2, 1@3/4)
1/2: eat 1, carry 1 (8@1/2, 1@3/4)
  1: drop 1 (1/2 in stomach, 8@1/2, 1@3/4, 1@1)
1/2: repeat above 3 times (2@1/2, 1@3/4, 4@1)
1/2: eat 1, carry 1 (0@1/2, 1@3/4, 4@1)
  1: drop 1 (1/2 in stomach, 1@3/4, 5@1)
3/4: carry 1 (1/4 in stomach, 0@3/4, 5@1)
  1: drop 1 (stomach empty, 6@1)
  1: move 3 miles futher in using previous answer

      [download]

      - tye        

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