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There are four main towns in Lateralia. We will call them A, B, C and D. They lie at the corners of a ten-mile square. In order to improve communications between the towns, the Lateralian Department of Transport decided to build a new road linking all four towns together. Because they had very little money, it was decided that the new road system should be as short as possible and still allow access from any one town to any other. The engineers came up with three designs shown below.

 A______B A______B A B | | | | \ / | | | | \/ | | | | /\ |______| | | / \ C D C D C D  

Number one uses 40 miles of road, number two uses 30 miles of road, and number three uses 28.3 miles of road. The designers naturally recommend plan number three because it employed the smallest road area and, therefore, cost the least. However, when they submitted their plan to the Minister of Finance, he accused them of extravagance and quickly pointed out a better design that required even less total road surface. What was his superior solution?

Guest May 4, 2015

Best Answer 

 #1
avatar+26329 
+8

Because you are Anonymous we can't see your images (I recommend that you register).  However, I think the minimum road length configuration will probably look something like the following:

 road configuration

.

Alan  May 4, 2015
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15+0 Answers

 #1
avatar+26329 
+8
Best Answer

Because you are Anonymous we can't see your images (I recommend that you register).  However, I think the minimum road length configuration will probably look something like the following:

 road configuration

.

Alan  May 4, 2015
 #2
avatar+78750 
0

Very nice, Alan....!!!!

 

 

  

CPhill  May 4, 2015
 #3
avatar+26329 
+5

Thanks, but I can't really take credit for it - it's a well-known optimisation problem, I've come across various versions of it dozens of times before.

.

Alan  May 4, 2015
 #4
avatar+78750 
0

I've never seen it before...but...it looks like a good "tavern bet"  problem....!!!!!

 

  

CPhill  May 4, 2015
 #5
avatar+91049 
0

Too bad if there is a cliff in the way :/

Melody  May 4, 2015
 #6
avatar+26329 
+5

Here's a photo of the soap film solution:

 soap film:

Alan  May 4, 2015
 #7
avatar+78750 
+5

Ah, Melody.....I think you're making a mountain out of a molehill....LOL!!!

 

 

  

CPhill  May 4, 2015
 #8
avatar+1068 
+5

Good job, Alan!

What am I doing here...?

civonamzuk  May 4, 2015
 #9
avatar+91049 
0

I don't know civonamzuk - I expect you are joining in the fun like everyone else  :)

Melody  May 4, 2015
 #10
avatar+91049 
0

Why do soap bubbles 'need' to joint to, well, anything?

Melody  May 4, 2015
 #11
avatar+26329 
+5

They stick to the wet posts and the wet glass (and themselves) via surface tension.

.

Alan  May 4, 2015
 #12
avatar+91049 
0

Thanks Alan :)

Melody  May 4, 2015
 #13
avatar+78750 
0

Apparently....they just don't stick well to "forum"  posts......

 

  

CPhill  May 4, 2015
 #14
avatar+1068 
0

I meant it as a joke, Melody.

civonamzuk  May 4, 2015
 #15
avatar+91049 
+5

ok Civonamzuk  :))

 

I have added this to the Sticky topic "Great answers to Learn From"

If anyone would like to take an interest in organising some of our reference material that would be great.

Melody  May 5, 2015

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