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The Ol' Bulb Drop: Newsletter Challenge (January 2019)

Posted December 30, 2018 5:01 PM
Pathfinder Tags: bulb drop challenge question

This month's IEEE GlobalSpec newsletter challenge is:

You’re given 20 destructible light bulbs, and a building with 100 floors. How do you determine the highest floor from which a light bulb may be dropped without breaking, using as few drops as possible?

Extra credit: How do you solve this puzzle having only been given two bulbs?

And the answer is:

First, it helps to define some common properties for this problem:

- If a light bulb is dropped from a given floor and breaks, then any other light bulb will also break if dropped from that or any higher floor.

-If a light bulb is dropped from a given floor and does not break, then neither it nor any other light bulb will break if subsequently dropped from that or any lower floor.

-A light bulb may be dropped any number of times until it breaks, after which it is unusable and cannot be dropped again.

From here out, let f = the building’s total floors and b = the number of bulbs available, and d = the number of drops required.

If we have 20 bulbs – which is more than enough to determine the number of required drops – a simple binary search will suffice. We start by dropping a bulb from the 50th floor. If it breaks, we move to the 25th floor and drop again; if it doesn’t, we move to the 75th floor and drop again.

Therefore, the maximum number of drops is:

or in this case, seven drops.

Extra credit:

Things get more interesting if we have two bulbs – fewer than the maximum number of drops determined above. In this case we need to flip the problem and, given the maximum number of drops d, solve for f instead.

Imagine conducting the first drop from floor k. If the bulb breaks, there must be at most f (d - 1, b - 1) floors below k. If it does not break, there be at most f (d – 1, b) floors above k.

Therefore, f (d,b) satisfies

And we can show via the recursive formula that:

This formula gives a solution to this problem with any amount of floors and bulbs. Given 100 floors and two bulbs, we need 14 drops in a worst-case scenario.

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#1

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/30/2018 5:55 PM

I would half the floors and test for break/ no break results starting with the 50th floor...

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#6
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 4:26 PM

It may be possible to reduce the number. If bulb 1 is dropped from floor 100, the number of floors it passes before terminal velocity can be observed. Subsequent tests can follow your reasoning from the 3rd (or whatever height it is to treach terminal velocity) floor.

A slight aside : The question implies an indestructable lightbulb exists. I'm baffled, because Ive yet to find anything in the house I cannot break.

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#37
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/08/2019 9:54 AM

Regarding your slight aside, the question says DEstructable

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#38
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/09/2019 4:11 PM

You're quite correct, though stating 'destructable' is not needed unless the question setter considers that indestructable light bulbs exist.

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#39
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/29/2019 12:25 PM

I find that if I stand on a chair to change a light bulb & drop it, It breaks, so 9Ft max.

Bazzer.

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#2

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/30/2018 6:30 PM

Binary search starting at 50. It shouldn't take more than 7 bulbs, probably less.

If you have 2 bulbs, start at 2,4,6, ... until it breaks. Then drop the other one from the floor below.

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#3

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 9:31 AM

I've got this solved with zero bulbs.

The answer is 1 floor or less.

I know because I've been doing this test for many years.

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#4
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 2:35 PM

You're stuck in an incandescent frame of mind....

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#5
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 2:54 PM

It said lightbulb. It didn't say solid-state device.

I certainly don't see a light bulb in your picture.

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#8
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 5:15 PM

How bout this?

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#9
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 10:01 PM

If that's one of those LEDs with the glass envelope/bulb? I've used and broken those too. and my answer is unchanged.

They are destructable at one story or less.

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#13
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/01/2019 1:03 AM

They have a plastic bulb...

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#16
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/01/2019 7:10 PM

Light bulbs by definition are glass.

Semantics? I think not

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#27
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 3:22 PM

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#28
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 7:38 PM

.. with inert gas and filiment!?*)

... glass LEDs... Oh my sure

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#18
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 5:48 AM

I have a light bulb like that which was dropped ( or dropped on) from several floors and is still functioning fine. Oh that is right they said without breaking. It broke but was not destroyed. Still works fine without outer decorative shell.

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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 4:50 PM
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#22
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 12:20 PM

That video made areas of my body feel weird.

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#10

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 10:45 PM

Use a Fibonacci search to minimize the number of drops

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#11

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

12/31/2018 11:01 PM

You drop one from any of the 100 floors, then save the other nineteen.

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#12

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/01/2019 12:41 AM

From the "destructible light bulbs" being the main point of test, and as it doesn't say if this building has a lift, it would be a simple matter to begin this test at the first floor (less energy walking up) and if it breaks you still have one and you know the bulb's failure height.

If it doesn't break...pick it up and wander up to the 2nd floor and repeat...wish they'd put a lift in this building!

If it doesn't break...pick it up and wander up to the 3rd floor and repeat...where's the lift?

And repeat upward until the ultimate failure or the 100th floor, whichever comes first. At which point you will become an olympic grade athlete and still have one bulb.

Wouldn't the continued dropping weaken the bulb? Probably but so would dropping it from waist height standing on the ground floor - if the ground floor doesn't have lush carpet it will break right there and then and your olympic dreams are as shattered as the bulb.

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#15
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/01/2019 2:25 PM

There's a little man that runs out and steals the bulb before you can get back down the stairs...

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#23
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 12:24 PM

Because there is no Lift!

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#19
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 8:19 AM

This is the correct answer. Start at the bottom and work up until one breaks.

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#14

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/01/2019 1:43 PM

I think you start at Floor 64, then go up or down in floors by decreasing powers of 2.

So if the bulb doesn’t break, you’d go to 96, then either up to 100 or down to 80, etc.

If the bulb breaks at 64 you go down to 32, then either up to 48 or down to 16, etc.

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#17

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 1:00 AM

Mathematically the given question is can be solved by the below formulae.

2 n = 100.

i.e. n ≅ 6 to 7 tries.

Hence, maximum 6 to 7 tries will able to figure out the floor from which the dropping the bulb without breaking.

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#29
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/03/2019 1:32 AM

And dropping from 50th floor and if pass 75 floor else 25th floor and goes on ....

within 6 tries you will able to figure out, worst scenario 7 tries.

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#20

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 9:13 AM

Start at the bottom floor going up using the same bulb until it breaks.

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#21

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 12:14 PM

What type of "Light Bulb"?

Results will vary.

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#24

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 12:31 PM

The Ol' Bulb Drop (20 destructible light bulbs & building with 100 floors). I would start at the 5th floor. If bulb broke I would go to the 3rd floor and drop another. If bulb broke again I would go to the 1st floor, where I imagine the bulb would break there too. If it did not break I'd go back to the 2nd floor and the bulb would either break or not break. If not your answer would be the 2nd floor. If bulb did not break at the original 5th floor then I'd continue to the 10th floor. Whether it broke or not determines whether I proceed up or down. The Ol' bulb drop with 2 bulbs & 100 floors. I would already know from the first experiment at what floor the bulb could be dropped and not break.

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#25

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 1:00 PM

Start at Floor 50.

If it does not break, increase 10 to 60, if it breaks then drop each floor from 60 to 50 to find the sweet spot, if it does not break go up 10.

Or, Breaks on 50, Drop to 40. If it holds at 40 then up per floor one at a time until you find the sweet spot.

Max bulbs used 15 if: 50-100 or 50-10

Truth: Most bulbs don't survive a 6' ladder drop.

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#26

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/02/2019 1:36 PM

2 questions. First: How do you define breakage? Breaking the glass envelope or knocking the filament out? Second: What surface will it land on? Concrete, grass, or something else?

My own experience with incandescent bulbs, when they are lit, is just a few feet if that much.

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#30
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/03/2019 4:24 PM

With an incandescent bulb you don't need to drop it at all...If it has been on for a while and the filament is hot it just takes a good smack for the element to destruct....Good riddance!

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#31

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/04/2019 12:21 PM

Er...is the bulb being dropped outside the building ? If It's dropped inside an appartment, the answer is either floor 100 or indeterminate. Possibly.

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#32

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/04/2019 1:04 PM

I like the out of the box thinking!

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#34
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/06/2019 8:19 PM

It's that longstanding tradition of arguing semantics on these Newsletter Challenges. Half the benefit would be lost if there was no scope to do so.

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#33

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/05/2019 7:12 AM

A standard incandescent light bulb? 1 floor will suffice.

Anything more than that is just another story.

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#35
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/06/2019 8:28 PM

I fear we have got to that 'how many people does it take to change a lightbulb' stage.

My favourite answer is folk singers - 1 to change the bulb and another 10 to sing about how good the old one was.

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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/07/2019 8:36 AM

Answer is posted.

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#40

Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/29/2019 4:41 PM

In this puzzle, no mention has been made of the landing ground, concrete to a pond of water

Onto concrete, one floor is too high, into a pond of water, they will probably survive from floor 100.

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#41
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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

01/31/2019 11:21 PM

I'm with you on that one, but may break hitting water, I was thinking more of a heavy snow 2 - 3ft deep.

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Re: The Ol' Bulb Drop: Newsletter Challenge (January 2019)

02/01/2019 6:03 PM

We have all assumed the bulb was not East European made. Read on for the astonishing story of the late Vesna Vulovic.

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