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#1 2014-08-12 02:23:07
- anna_gg
- Member
- Registered: 2012-01-10
- Posts: 232
Electrical fuse board
Hi everyone!
A computer data center is controlled by an electrical fuse board consisting of 15 fuses in one row.
The power in the data center goes off if any two consecutive fuses are in the OFF position (for example, if Y is ON and N is OFF, the power goes off if we have YYNNYYYYYYYYYYY but not if we have YNYNYNYNYNYYYYY). In how many different ways can we arrange the fuses, so as to always have power?
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#2 2014-08-12 02:39:08
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Electrical fuse board
Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2014-08-12 03:54:14
- anna_gg
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- Registered: 2012-01-10
- Posts: 232
Re: Electrical fuse board
How?
(I am neither a physicist nor a respectable mathematician, thus not contemptuous about proof...)
Last edited by anna_gg (2014-08-12 03:58:09)
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#4 2014-08-12 04:05:25
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Electrical fuse board
It is sort of okay to not be a mathematician and darn right noble not to be a physisict, but you must be an experimentalist/programmer.
The simplest idea is to play spot the pattern. It is one of the cornerstones of doing Experimental Math.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2014-08-12 04:29:49
- phrontister
- Real Member
- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,877
Re: Electrical fuse board
Hi Bobby,
I played Experimental Maths with it as you suggested and got your answer after spotting the pattern.
If there had been 16 fuses my answer would have been...
Last edited by phrontister (2014-08-12 04:35:34)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#6 2014-08-12 04:37:21
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Electrical fuse board
The way to an analytical solution is just to recognize those numbers.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2014-08-12 04:48:33
- phrontister
- Real Member
- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,877
Re: Electrical fuse board
I may never have recognized those numbers had I not found out about their popularity in a particular field.
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#8 2014-08-12 04:51:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Electrical fuse board
The physicists runs around the lab screaming that he is God. The mathematician stares up at the ceiling muttering to himself but the EM guy is blessed because he sees the answer.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2014-08-12 04:57:40
- phrontister
- Real Member
- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,877
Re: Electrical fuse board
Hehe! 
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#10 2014-08-12 04:59:18
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Electrical fuse board
How are things in the land of tomorrow?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#11 2014-08-12 05:56:51
- phrontister
- Real Member
- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,877
Re: Electrical fuse board
They are really good right now, I think. I'll find out for sure tomorrow how they are...that is, if I can somehow break that old adage.
Whatever...busy as always, and enjoying life.
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#12 2014-08-12 05:59:12
- anna_gg
- Member
- Registered: 2012-01-10
- Posts: 232
Re: Electrical fuse board
Hmmm... Fibonacci numbers...
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#13 2014-08-12 06:11:17
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Electrical fuse board
Whatever...busy as always, and enjoying life
That is good. At 27 the world is yours.
Hmmm... Fibonacci numbers...
Yes, with initial conditions of 1 and 2 instead of 1 and 1.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2014-08-12 06:53:07
- anna_gg
- Member
- Registered: 2012-01-10
- Posts: 232
Re: Electrical fuse board
Hmm now I see: If we had a string of length 2, the options would be YY, YN, NY (3 options).
For length 3, it would be YYY, YYN, YNY, NYY, NYN (5 options).
For length 4: YYYY, YYYN, YYNY, YNYY, YNYN, NYYY, NYYN and NYNY (8 options) and so on (13, 21 etc), thus for length 15 it would be 1597.
Thank you guys for your assistance!!
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#15 2014-08-12 09:21:13
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Electrical fuse board
Hi anna_gg;
You are welcome.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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