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A really simple connect-the-dots problem


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16 replies to this topic

#1 bonanova

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Posted 12 May 2012 - 06:49 AM

A classic puzzle notes that 3 miles of road is sufficient to connect four cities situated on the corners of a square one mile on a side. Yes, the cities are really small; point-like, for our purposes. The question is then asked: what length of road(s) is necessary to connect them? I.e. the shortest distance of road(s) required.
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#2 Thalia

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Posted 12 May 2012 - 07:07 AM

Spoiler for

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#3 Ryo

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Posted 12 May 2012 - 04:20 PM

Spoiler for 1.78

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#4 fabpig

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Posted 12 May 2012 - 05:01 PM

Spoiler for I could be missing something.....

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#5 bushindo

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Posted 12 May 2012 - 07:22 PM

A classic puzzle notes that 3 miles of road is sufficient to connect four cities situated on the corners of a square one mile on a side. Yes, the cities are really small; point-like, for our purposes. The question is then asked: what length of road(s) is necessary to connect them? I.e. the shortest distance of road(s) required.


Here's an attempt,
Spoiler for attempt

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#6 Yoruichi-san

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Posted 12 May 2012 - 08:52 PM

Here's an attempt,

Spoiler for attempt


I think you're right
Spoiler for Yay, calculus

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Women are definitely stronger. We are [Fe]males, after all...

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#7 WitchOfSecrets

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Posted 13 May 2012 - 03:34 AM

Spoiler for You can't get any shorter than this.

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#8 bonanova

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Posted 13 May 2012 - 05:55 AM

Spoiler for You can't get any shorter than this.


Very clever. I like this solution so much that I submitted it to the combined Town Boards of the ABCD Municipality for approval. They texted me back and said they were willing to proceed, even to bear the cost of all that additional asphalt, provided that

Spoiler for we also submit

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 Yoruichi-san

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Posted 13 May 2012 - 06:13 AM

Very clever. I like this solution so much that I submitted it to the combined Town Boards of the ABCD Municipality for approval. They texted me back and said they were willing to proceed, even to bear the cost of all that additional asphalt, provided that

Spoiler for we also submit


Spoiler for Roundabout soln...

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.


#10 WitchOfSecrets

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Posted 13 May 2012 - 06:30 AM

bonanova: No problem!

Spoiler for Divider line

Edited by WitchOfSecrets, 13 May 2012 - 06:33 AM.

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