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# Lightbulb tester

## Question

You were just hired to work at a lightbulb factory as a lightbulb tester. They just invented, they believe, a lightbulb that can resist breaking when dropped from most heights. They have asked you to test their product and find its threshold by dropping the new product out of their 100 floor building. Realizing that this is your first assignment at the company and also that these bulbs are expensive, you will want to test it accurately but not want to waste the product. What is the best way to test this product?

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This is a chestnut.

But since no one has jumped in with the answer, I'll give it another life.

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Drop a single light bulb from each successive floor from the bottom until it breaks or you reach the 100th floor. This only breaks at most 1 light bulb.

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Drop a single light bulb from each successive floor from the bottom until it breaks or you reach the 100th floor. This only breaks at most 1 light bulb.

Aren't you assuming that there are no defective lightbulbs? Surely not every bulb is made exactly alike (some variance)

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Drop a single light bulb from each successive floor from the bottom until it breaks or you reach the 100th floor. This only breaks at most 1 light bulb.

also this is not the most efficient way as you may not be done until the 97th floor or something.

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Define the word "best", as conserving light bulbs does not seem to be it, despite them being expensive.

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Best In the sense of using the fewest amount of bulbs and taking the least amount of time but still getting accurate results.

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If I assume that I may possibly break all the light-bulbs I can maximise accuracy and time

I could start on the 50th floor dropping 1/7 of the light bulbs

If I break more than 50% I could then go down 25 floors

If I break less than 50% I go up 25 floors

If I break exactly 50% I complete my assessment and demand a raise

else I then drop 1/6 of the remaining light bulbs

...

There also may be a way to further increase accuracy by taking note of the percentage of broken light bulbs on previous floors

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Sorry

There also may be a way to further conserve light bulbs by taking note of the percentage of broken light bulbs on previous floors

from the 50th floor calculate

round ((50 - Percentage of light bulbs broken from this height ) * 7/50)

If more than 50% break go down 25 minus this value floors

if less than 50% break go up 25 plus this value floors

basically if they all break go down 32 floors increasing the survivability of the remaining light bulbs without increasing the number of required tests. The reason I would not do this if 51% break is the higher chance that you may hit 50% be able to bail early without further tests

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Sorry

There also may be a way to further conserve light bulbs by taking note of the percentage of broken light bulbs on previous floors

from the 50th floor calculate

round ((50 - Percentage of light bulbs broken from this height ) * 7/50)

If more than 50% break go down 25 minus this value floors

if less than 50% break go up 25 plus this value floors

basically if they all break go down 32 floors increasing the survivability of the remaining light bulbs without increasing the number of required tests. The reason I would not do this if 51% break is the higher chance that you may hit 50% be able to bail early without further tests

does starting at the 50th floor produce the best results?

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As you could start anywhere between 36 and 64 with the same amount of drops the 50th floor will give you the most flexibility for later on

Edited by phaze

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