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Light-bulb Problem


Best Answer BMAD, 10 July 2013 - 08:01 PM

My answer is not very different from BobbyGo's, mainly to recognize two switches light one bulb from each of the two groups, thereby eliminating analysis of some non-occurring cases. It took me awhile to conclude the 1- and 3-switch bulbs were different, then the rest fell quickly in place.

I'll share my BA with BG. ;)

 

 

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#1 BMAD

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Posted 17 June 2013 - 10:15 PM

This is a modified version of the famous light-bulb problem.  

 

There are three switches in the hallway.  turning on the switches in different combinations cause different light-bulbs in the room to turn on. There are six light-bulbs and from turning on all of the possible combinations, each light-bulb is turned on at most twice (in other words there are only two ways to turn on a light-bulb).  We need to map the switches to the light-bulbs.  

 

The only things we know is that flicking 1 switch causes 1 light-bulb to turn-on, flicking 2 switches causes 2 to turn-on, and flicking all 3 cause three light-bulbs to turn-on and if a switch turns on a light-bulb, that switch must be on to turn it on again (even if flicking 2 switches).

 

What is the fewest number of 'tests' needed to effectively map the light-bulbs to the switches?


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#2 Nins_Leprechaun

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Posted 18 June 2013 - 07:34 AM

Missed the last point and am starting again

Edited by Nins_Leprechaun, 18 June 2013 - 07:36 AM.

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#3 Nins_Leprechaun

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Posted 18 June 2013 - 08:07 AM

I'm still getting the same brutish answer. However, either the question is leading me on with useless information or there's a better solution

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#4 BMAD

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Posted 18 June 2013 - 02:02 PM

testing the 2 combos won't tell you which single switch turns on a single light-bulb and which three switch turns on which three switch combo.


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#5 Nins_Leprechaun

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Posted 18 June 2013 - 07:32 PM

I may have misunderstood something, but here is a better explanation of what I meant

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#6 BobbyGo

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Posted 18 June 2013 - 10:02 PM

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Edited by BobbyGo, 18 June 2013 - 10:05 PM.

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#7 Nins_Leprechaun

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Posted 19 June 2013 - 03:09 AM

testing the 2 combos won't tell you which single switch turns on a single light-bulb and which three switch turns on which three switch combo.


Ahh yes, now I understand what the confusion here was
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#8 jordge

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Posted 19 June 2013 - 04:49 PM

Spoiler for My answer


Edited by jordge, 19 June 2013 - 04:49 PM.

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#9 BobbyGo

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Posted 19 June 2013 - 08:38 PM

Spoiler for

 

I had considered testing for heat and testing for light to count as two different tests because you would need to use two different senses to acquire the information.  If this is correct, I'll stick with my answer above.

 

If this is not the case, I'll change my answer to the one below.

 

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#10 jordge

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Posted 20 June 2013 - 03:50 PM

BobbyGo - I think your assumption about the light configurations is wrong. When I read the OP, I took it literally in that if a light is on, a certain switch must be up, exclusive of any other switches that may be up.  This would prevent the possibility of switch 1 operating light A individually but then the switch 2 and 3 combination also illuminating Light A.

 

OP - Clarification?


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