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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Green Puzzle Cards
[SOLVED] #121- Seven Bridges.
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GasparLewis
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Joined: 19 Nov 2005
Posts: 474
Location: vicinty of NYC

 		[SOLVED] #121- Seven Bridges.
In the old town of Perplex City are seven bridges crossing the river Mazy. In the past, visiters were often asked whether they could go for a walk that would cross all seven bridges once, but not any of them twice. Can you?



All I have to say is:
Spoiler (Rollover to View):
Could Euler do it in Königsberg? Eh? Eh?


Meaning that the answer is:
Spoiler (Rollover to View):
no


PostPosted: Fri Nov 25, 2005 1:30 am
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spugmeistress
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Joined: 22 Feb 2005
Posts: 460
Location: manchester, uk

 		Not meaning to be pedantic, as you gave a very fine answer, however my quarrel is more with the cards wording itself.
Surely you could easily go for a walk whereever you liked, you just might not end up where you want to be?
Nowhere does it mention having to return to the point that you started...

rach =)

PostPosted: Fri Nov 25, 2005 6:43 pm
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Kvasir
Boot

Joined: 15 Oct 2005
Posts: 48

 		Getting back to the starting point isn't a requirement. The only requirement is to walk across all seven bridges once and only once.

PostPosted: Sun Nov 27, 2005 11:26 am
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GasparLewis
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Joined: 19 Nov 2005
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Location: vicinty of NYC

 		Of course, but:

Spoiler (Rollover to View):
Start and finish aside, it's still impossible. Even allowing yourself to finish on an island still is an impossibility. It's all because of that mid-island bridge. Because of it, you have to change islands in crossing, and that throws off any plans whatsoever. Doesn't really matter; it just cannot be done.

Unless they're implying you can wade through the river. Laughing


PostPosted: Sun Nov 27, 2005 1:26 pm
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Daffy889
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Joined: 25 Aug 2004
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Location: South Australia

 		There doesn't appear to be anything on this card to say that you can't use the bridge further down the River as part of your walk, or the tunnels underneath it for that matter. Still, I expect that's just bad wording on the part of the card creator.
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PostPosted: Sun Nov 27, 2005 1:40 pm
Last edited by Daffy889 on Thu Jul 20, 2006 4:37 pm; edited 1 time in total
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spugmeistress
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Joined: 22 Feb 2005
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Location: manchester, uk
GasparLewis wrote:
Of course, but:

Spoiler (Rollover to View):
Start and finish aside, it's still impossible. Even allowing yourself to finish on an island still is an impossibility. It's all because of that mid-island bridge. Because of it, you have to change islands in crossing, and that throws off any plans whatsoever. Doesn't really matter; it just cannot be done.

Unless they're implying you can wade through the river. :lol:


i get it now... i swear i managed it and ended up on the middle island the other day but i must have made a mistake cos i can't do it for the life of me now.

rach =)

PostPosted: Mon Nov 28, 2005 8:53 pm
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doublecross
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Joined: 25 Jul 2005
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Location: London, UK

 		Explanation:

Spoiler (Rollover to View):
Make the bridges lines and the land areas dots (i.e. 7 lines and 5 dots). You now have yourself a 'graph' (as it is called in mathematics).

Except for your starting and ending point, you will enter and leave each dot some number of times. Therefore, each intermediate dot must have an even number of lines coming from it. If the starting and ending point are different, they will have an odd number of lines coming from them. If they are the same, then all dots will have an even number of lines coming from them.

Conclusion - for a graph to be traversable without going over any lines twice, there can only be either zero or two dots with an odd number of lines coming from them. The famous Koningsberg Bridges problem, of which this is a copy, has all five dots with an odd number of lines coming from them. Therefore, it is not traversable.

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xx

PostPosted: Tue Nov 29, 2005 7:23 am
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Nicolaas
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Joined: 15 Feb 2006
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Location: Amsterdam

 		Why 'in the past'? Was one of the bridges built later? Clue?

PostPosted: Tue Feb 21, 2006 8:23 pm
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European Chris
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Joined: 19 Jul 2005
Posts: 1264
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Nicolaas wrote:
Why 'in the past'? Was one of the bridges built later? Clue?


I assume that's because it's now been mathematically proven you can't and all the PPC residents would realise this is a futile question and consquently wouldn't ask it.
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PostPosted: Tue Feb 21, 2006 8:33 pm
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Nicolaas
Greenhorn


Joined: 15 Feb 2006
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Location: Amsterdam

 		Koenigsberg = Seven Bridges
This is what I found on Internet just now (see link):

Königsberg is a next city from Danzig. It is also beautiful and prosperous like here. But it is worldly famous for the Königsberg Bridges Problem, which means 'The river Pregel (Mazy?) divides the city into four separate landareas. Seven bridges connect them. People in Königsberg love to take walks along the river and the island for some time, and it has became a Sunday tradition to take the walk of seven bridges. Many of them wondered if it were possible to take a journy across all seven bridges without having to cross any bridge more than once. The elderly say, 'We could do that easily, but then there were only six bridges.' Now many people want to find the solution. So they walk in town over and over and they don't have time to listen to music.' Mr. Goldberg said, 'People there are addicted to this kind of problem or Philosophical matters. I wish my son could live with music like in Danzig.' Later I made a handcopy of the easier peaces from Clavierübung 1, and presented it to this kid named Johann Gottlieb Theophilus Goldberg."

PostPosted: Tue Feb 21, 2006 8:49 pm
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stockton
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Joined: 22 Jul 2006
Posts: 4
Location: Bangor N.I.

 		It is only looking for a yes or no answer!! Laughing

PostPosted: Tue Jul 25, 2006 1:27 pm
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JTony
Veteran


Joined: 11 Oct 2005
Posts: 88
Location: San Francisco, CA

 		This Card Made me So Mad!!!
AAARRRRRGGGGGG!!!
I am so mad at this card. I assumed that it was possible from the fact that I didn't expect a card to simply be looking for a yes or no answer.

Spoiler (Rollover to View):
Assuming it was possible and not wanting to spoil the solution, I wracked my brains on it for 3 days, thinking about it in the shower, thinking about it while driving, thinking about it while having conversations with other people, thinking about it constantly. Only to find out in the end that it is impossible!


Almost enough to put me off of puzzles altogether...

Almost, but not quite.

Grrrr. Evil or Very Mad
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PostPosted: Wed Aug 23, 2006 3:29 pm
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