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Lightbulb tester on PGH (puzzle growth hormone)


Best Answer phaze, 19 February 2013 - 12:00 AM

Spoiler for Solution
Go to the full post


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8 replies to this topic

#1 bonanova

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Posted 18 February 2013 - 10:54 PM

Taking the light bulb puzzle up a few notches:

 

When dropped from the fth floor of a building, Bonanova's Brilliant Lightbulbs uniformly will break, but not if dropped from a lower floor. You are tasked with determining f using a nearby 1000-story building. Formulate an efficient strategy for determining f, and then request only as many BBLs as are needed to carry it out, covering the strategy's worst case.

 

Here's one strategy:

 

Drop a BBL from randomly chosen floors.

Worst case requires 1000 drops.

Ask for 1000 BBLs.

 

But you can do better.

 

What's the number of BBL's needed to determine f with the fewest number of drops?

You may assume that a 1000-story building is tall enough for this task.


Edited by bonanova, 18 February 2013 - 11:35 PM.
Clearly state the strategy must be optimally efficient with respect to number of drops

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 phil1882

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Posted 18 February 2013 - 11:00 PM

Spoiler for 1 bulb

Edited by phil1882, 18 February 2013 - 11:01 PM.

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#3 bonanova

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Posted 18 February 2013 - 11:26 PM

Yes. Absolutely correct. And I did not ask the question that I intended to ask. :wacko: 

[Where are the puzzle testers when you need them?]

 

Restate:

 

How many BBLs are needed to determine f with the fewest possible drops?

 

To be sure that I mean to say when I ask what I think I mean to ask, I'll break it down.

You have n bulbs; there is a strategy for determining f in the fewest drops.

 

Phil's answer is correct for n=1, and worst case it takes 1000 drops.

If you have 2 bulbs, there is a strategy for determining f with fewer than 1000 drops.

Given 3 bulbs, you could get f with even fewer drops.

At some point, say nf, more bulbs won't reduce the number of needed drops.

 

What is nf ?

 

I'll try to rescue the OP with an edit.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 phaze

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Posted 19 February 2013 - 12:00 AM   Best Answer

Spoiler for Solution

Edited by phaze, 19 February 2013 - 12:02 AM.

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#5 bonanova

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Posted 19 February 2013 - 02:32 AM

Right on.

Use the elevator, make life easy. ;)
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 phil1882

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Posted 19 February 2013 - 02:49 PM

Spoiler for optimal solution, 8 bulbs.

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#7 phil1882

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Posted 19 February 2013 - 03:20 PM

apologies some numbers wrong.

Spoiler for

Edited by phil1882, 19 February 2013 - 03:25 PM.

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#8 jamieg

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Posted 20 February 2013 - 02:42 AM

Spoiler for For n=2:


Edited by jamieg, 20 February 2013 - 02:47 AM.

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#9 BMAD

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Posted 20 February 2013 - 06:21 AM

Spoiler for statistics vs Math

Edited by BMAD, 20 February 2013 - 06:21 AM.

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