City Planning

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MartianInvader
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City Planning

Postby MartianInvader » Tue Oct 30, 2007 11:53 pm UTC

Here's a puzzle inspired by (though not requiring) some rather hefty mathematics:

A city planner is given some odd requirements by a rather eccentric governor for the city he's designing. There are 4 requirements:

- Each street corner must have exactly 3 streets (not the usual 4). Of these streets, one must be one-way leaving the intersection, one must be one-way entering the intersection, and one must be two-way.

- Anyone driving five consecutive blocks down one-way streets will find themselves back where they started.

- Anyone driving for six blocks, alternating one- and two-way streets as they go, will find themselves back where they started.

The problem: What is the governor's favorite sport?


Edited to be less obvious
Last edited by MartianInvader on Wed Oct 31, 2007 1:58 pm UTC, edited 1 time in total.
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

ptveite
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Re: City Planning

Postby ptveite » Tue Oct 30, 2007 11:56 pm UTC

Spoiler:
soccer


Hix
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Re: City Planning

Postby Hix » Wed Oct 31, 2007 12:07 am UTC

Agreed, soccer. Alternately, the conditions are satisfied by having no streets at all.

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MartianInvader
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Re: City Planning

Postby MartianInvader » Wed Oct 31, 2007 12:13 am UTC

Indeed. Hm, 3 answers in 15 minutes... I guess it was too easy with the sports thing, maybe I should have just left out the 4th condition and instead asked what familiar graph the streets make.

Anyhoo, well done!
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

ptveite
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Re: City Planning

Postby ptveite » Wed Oct 31, 2007 1:32 am UTC

MartianInvader wrote:Indeed. Hm, 3 answers in 15 minutes... I guess it was too easy with the sports thing, maybe I should have just left out the 4th condition and instead asked what familiar graph the streets make.

Anyhoo, well done!


Ya, I think it might be better if the question seemed like more of a non-sequitur, just nix the 4th criteria and immediately ask what they guy's favorite sport is.

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Macbi
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Re: City Planning

Postby Macbi » Wed Oct 31, 2007 1:09 pm UTC

A man starts at his campsite.
He goes one kilometre south, where he sees a bear.
He is so scared that he runs one kilometre west.
He then returns to his campsite by walking one kilometer north.

What colour was the bear?
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pr1mu5
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Re: City Planning

Postby pr1mu5 » Wed Oct 31, 2007 1:14 pm UTC

Spoiler:
white

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crazyjimbo
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Re: City Planning

Postby crazyjimbo » Wed Oct 31, 2007 1:18 pm UTC

MartianInvader wrote:Here's a puzzle inspired by (though not requiring) some rather hefty mathematics:

A city planner is given some odd requirements by a rather eccentric governor for the city he's designing. There are 4 requirements:

- Each street corner must have exactly 3 streets (not the usual 4). Of these streets, one must be one-way leaving the intersection, one must be one-way entering the intersection, and one must be two-way.

- Anyone driving five consecutive blocks down one-way streets will find themselves back where they started.

- Anyone driving for six blocks, alternating one- and two-way streets as they go, will find themselves back where they started.

What is the governors favourite allotrope?


Fix'd for XKCD.

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MartianInvader
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Re: City Planning

Postby MartianInvader » Wed Oct 31, 2007 2:01 pm UTC

Ok, I've changed the statement of the problem to be a bit less obvious. If anyone's curious, the math concept that inspired this was that of a Cayley Graph (wikipedia has a nice writeup on what these are). The problem is actually asking you to find the Cayley graph of the group with presentation <a, b | a^2, b^5, (ab)^3>.
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!

Nate_W
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Re: City Planning

Postby Nate_W » Wed Oct 31, 2007 4:29 pm UTC

So, I read the problem after the 4th criteria was gone, and it was still pretty obviously soccer. But can I ask what the 4th criteria was?

Token
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Re: City Planning

Postby Token » Wed Oct 31, 2007 5:06 pm UTC

Macbi wrote:A man starts at his campsite.
He goes one kilometre south, where he sees a bear.
He is so scared that he runs one kilometre west.
He then returns to his campsite by walking one kilometer north.

What colour was the bear?

The bear was actually a penguin.
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quintopia
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Re: City Planning

Postby quintopia » Wed Oct 31, 2007 5:08 pm UTC

Token wrote:The bear was actually a penguin.


Impossible! What's a penguin doing way up there?

And why did he switch from kilometres to kilometers midway through his trip?

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Macbi
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Re: City Planning

Postby Macbi » Wed Oct 31, 2007 5:15 pm UTC

quintopia wrote:
Token wrote:The bear was actually a penguin.


Impossible! What's a penguin doing way up there?

And why did he switch from kilometres to kilometers midway through his trip?

There are many different solutions to the problem, but bears are only likely to turn up in one.
He had entered American controlled space and changed spelling acordingly.
    Indigo is a lie.
    Which idiot decided that websites can't go within 4cm of the edge of the screen?
    There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

Token
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Re: City Planning

Postby Token » Wed Oct 31, 2007 5:43 pm UTC

quintopia wrote:
Token wrote:The bear was actually a penguin.


Impossible! What's a penguin doing way up there?

And why did he switch from kilometres to kilometers midway through his trip?

Bonus problem: a guy makes the same journey, but is scared by a ferocious penguin instead of a bear. At what latitude was his camp?
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quintopia
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Re: City Planning

Postby quintopia » Wed Oct 31, 2007 6:06 pm UTC

Ah, so he starts 1km north of the point at which the circumference around the axis is 1km?

Well, knowing that, calculating the latitude is trivial. . .I'm not going to bother.

(on another side note: what is a penguin doing so far inland?)

Hix
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Re: City Planning

Postby Hix » Wed Oct 31, 2007 6:22 pm UTC

quintopia wrote:Ah, so he starts 1km north of the point at which the circumference around the axis is 1km?

He could also be 1 km north of a line of latitude with circumference 1/2 km, or 1/3 km, etc.

Token
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Re: City Planning

Postby Token » Wed Oct 31, 2007 6:44 pm UTC

quintopia wrote:(on another side note: what is a penguin doing so far inland?)

Given that it was big enough to scare him into running an entire kilometer, I assume it was the penguin queen, who resides exactly at the South Pole.
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quintopia
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Re: City Planning

Postby quintopia » Wed Oct 31, 2007 9:09 pm UTC

Hix wrote:He could also be 1 km north of a line of latitude with circumference 1/2 km, or 1/3 km, etc.


True, so the answer to Token's bonus question is a parameterized function for latitude.

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MartianInvader
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Re: City Planning

Postby MartianInvader » Wed Oct 31, 2007 9:27 pm UTC

Token wrote:Given that it was big enough to scare him into running an entire kilometer, I assume it was the penguin queen, who resides exactly at the South Pole.


Ah, but if it was the penguin queen at the South Pole, then he didn't run at all, now, did he?
Let's have a fervent argument, mostly over semantics, where we all claim the burden of proof is on the other side!


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