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# Lightbulb tester on PGH (puzzle growth hormone)

### #1

Posted 18 February 2013 - 10:54 PM

Taking the light bulb puzzle up a few notches:

When dropped from the **f**^{th} 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

*and then request only as many BBLs as are needed to carry it out, covering the strategy's worst case.*

**f,**

__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

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

- Bertrand Russell

### #2

Posted 18 February 2013 - 11:00 PM

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

### #3

Posted 18 February 2013 - 11:26 PM

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

[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

*in the fewest drops.*

**f**

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 **n**_{f}, more bulbs won't reduce the number of needed drops.

What is **n**_{f }?

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

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

- Bertrand Russell

### #4

Posted 19 February 2013 - 12:00 AM Best Answer

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

### #5

Posted 19 February 2013 - 02:32 AM

Use the elevator, make life easy.

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

- Bertrand Russell

### #6

Posted 19 February 2013 - 02:49 PM

### #7

Posted 19 February 2013 - 03:20 PM

apologies some numbers wrong.

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

### #8

Posted 20 February 2013 - 02:42 AM

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

### #9

Posted 20 February 2013 - 06:21 AM

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

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