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#1 bonanova

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Posted 15 May 2013 - 01:26 AM

Enough with traveling salesman who hate long road trips.

Mario Andretti has joined the team, and he loves to drive!

 

His route today comprises eight towns, placed at the corners of an octagon.

Here are their coordinates:

salesman.gif

Edit: 7 and 8 are labeled incorrectly. They should be switched.

 

+---+-+-+

City x y

+---+-+-+

 1   0 2

 2   0 4

 3   2 6

 4   4 6

 5   6 4

 6   6 2

 7   4 0

 8   2 0

+---+-+-+

The inter-city distances, to save some calculations, are N-S and E-W distances of 6, along with four different diagonal distances of 2.828, 4.472, 5.657 and 6.083 6.325

 

If Mario begins driving at city 1 (coordinates 0 2) and drives until he has visited them all, how far will he be able to drive, and what city will he visit last?

 

If his objective is to return to his hotel in City 1 after visiting the other cities, how long of a trip could he accomplish?


Edited by bonanova, 15 May 2013 - 06:02 PM.
Switch 7 and 8 on the graph and correct 6.063 to 6.325

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#2 BMAD

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Posted 15 May 2013 - 01:29 AM

Enough with traveling salesman who hate long road trips.

Mario Andretti has joined the team, and he loves to drive!

 

His route today comprises eight towns, placed at the corners of an octagon.

Here are their coordinates:

attachicon.gifsalesman.gif

+---+-+-+

City x y

+---+-+-+

 1   0 2

 2   0 4

 3   2 6

 4   4 6

 5   6 4

 6   6 2

 7   4 0

 8   2 0

+---+-+-+

The inter-city distances, to save some calculations, are N-S and E-W distances of 6, along with four different diagonal distances of 2.828, 4.472, 5.657 and 6.083

 

If Mario begins driving at city 1 (coordinates 0 2) and drives until he has visited them all, how far will he be able to drive, and what city will he visit last?

 

If his objective is to return to his hotel in City 1 after visiting the other cities, how long of a trip could he accomplish?

 

Are you saying what is the greatest path?


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#3 bonanova

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Posted 15 May 2013 - 12:13 PM

Yes. But visit each city only once.
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#4 BMAD

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Posted 15 May 2013 - 02:10 PM

Yes. But visit each city only once.

Spoiler for depends

Spoiler for more likely


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#5 BobbyGo

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Posted 15 May 2013 - 03:26 PM

Spoiler for First Guess


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#6 bonanova

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Posted 15 May 2013 - 03:40 PM

Yes. But visit each city only once.

Spoiler for depends
Spoiler for more likely

Assume a network of straight roads connects every pair of cities.
I did not draw all the roads to keep the map uncluttered, but gave the distances.
That may have been a source of confusion.
Visit every city once and only once, using those roads.
No trips to Disney World.
Paths can cross.
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- Bertrand Russell

#7 bonanova

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Posted 15 May 2013 - 03:44 PM

Spoiler for First Guess


Good guess BG, but I found one a little longer.

 

This is the correct open route.

P.s. I think it's more challenging than finding the shortest route, which in this case is trivial.
If people like this genre I will post another.


Edited by bonanova, 15 May 2013 - 07:01 PM.
This solution is optimal.

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- Bertrand Russell

#8 kingofpain

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Posted 15 May 2013 - 03:48 PM

Spoiler for I think


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#9 BobbyGo

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Posted 15 May 2013 - 04:51 PM

Hmm... just noticed that the coordinates listed for points 7 (4,0) and 8 (2,0) are switched on the graph.  It labels 7 at (2,0) and 8 at (4,0).  Which set is correct?


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#10 Xavier

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Posted 15 May 2013 - 05:13 PM

on the graphic, 7 and 8 are inverted, also it seems the 6.083 distance whould have been 6.325

 

Spoiler for my take on it

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