View topic - [S2] [Dice Set] #071 The Cattle King

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Forum index » Diversions » Perplex City Puzzle Cards » PXC: Yellow Puzzle Cards

[S2] [Dice Set] #071 The Cattle King
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb

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PuzzledPineapple
Unfettered

Joined: 07 Apr 2005
Posts: 352

[S2] [Dice Set] #071 The Cattle King

Front:

Quote:

Bill had invited his flatmates Rob and Corey around to his family farm for the holidays. Having spent the day with his family whilst the others looked around the grounds, Bill was now sitting on the front porch relaxing and sipping a glass of Pinot Noir. The sun was just starting to set when Rob and Corey came up to him looking somewhat concerned. "We've just been out by your cattle pens. We noticed you'd used 17 fences to create 6 equal sized square pens. But the fences are all looking very worn and rusty. Won't it cost you a lot to replace them all?" "We'll be fine. We worked out a way to build 6 pens of equal size, though not necessarily the same size as the current pens, using fewer fences?" What's the smaller number of fences needed to build the new cattle pens?

Back:

Quote:

Perplex City Academy
Subsidiary Study Modules: 12a Earth Studies
Module Four: Technology
Course Coordinator: Clementine Friday

Earth technology is, in most fields, very like a rather backward version of Perplexian technology. Their medicine, for example, is quite clumsy. Even their much-loved cars require significant input from the drivers (although it is hard to see, from their technological capabilities in other fields, why this is the case).

Most striking of all is their lack of keys. How Earth people manage their day-to-day like without keys is somewhat mysterious. Portable communication tools do exist, but the universal functionality and compatibility necessary for a workable system of key integration is notably lacking.

Sample exam question:
Compare and contrast one of the following Earth inventions with its nearest Perplexian counterpart: (a) the magnetic compass and the Atkins-Archer wherebywhy; (b) the personal computer and the key; (c) cod liver oil and malt and Whipsmart Ice Quantum Cherry flavour.

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Posted: Fri Mar 09, 2007 4:47 pm

simonaubrey
Boot

Joined: 06 Dec 2005
Posts: 37

I got the same answer with 2 different configurations!!

Spoiler (Rollover to View):

12

using a hexagonal pattern and also by creating smaller (half size) squares but with some fences extending beyond the pen and not being used.

Posted: Tue Mar 13, 2007 12:03 pm

Jeraly
Greenhorn

Joined: 13 Mar 2007
Posts: 8
Location: Bristol, UK

Call me stupid but surely you could do it with

Spoiler (Rollover to View):

?

Know the answer isn't right as I tried it :/

Posted: Wed Mar 14, 2007 4:53 pm

aliendial
Unfictologist

Joined: 29 Sep 2002
Posts: 3438
Location: Far Far Away. Nowhere Near You. Really.

Well they all have to be the same size. And fences only connect at the ends (which is only implied, but explains why simon's answer is right). But I'm still not sure how just 7 would get you six pens - I could see 9, but the pens would be pretty skinny...

_________________
aliendial

Posted: Sun Mar 18, 2007 10:29 am

Eugenes Lair
Boot

Joined: 27 Feb 2007
Posts: 51

aliendial wrote:

I have a problem with this card, and it is that a great deal is implied but not explicitly stated. It's implied that the fences are solid and have to be connected at the edges, but it's not explicitly stated anywhere in the puzzle.

I'm unsure of the forum etiquette regarding wrong answers, so I'm going to hide the following discussions in spoilers.
If we don't assume that the fences have to be joined at the edges, then we can make 6 new pens with:

Spoiler (Rollover to View):

9 fences. We first make a square using 4 fences. We then divide the square into 6 strips by running the other 5 fences inside the square - all parallel and equally-spaced.
This produces 6 pens of equal size, each 1/6th the area of the original pens.

If we also don't assume that the fences are solid (e.g. they are barbed-wire), then we can make 6 new pens with:

Spoiler (Rollover to View):

7 fences. Again, we use 4 fences to make a square. We then run 2 fences internally - parallel and equally-spaced - to divide the square into 3 equal strips. We finally run another fence straight through the centre of the square, bisecting each of the previous 2 internal fences. This also creates 6 new pens of equal size, each 1/6th the area of the original pens.
From PM'ing Jeraly, I believe this is the arrangement implied in the earlier post.
(Please correct me if I've misunderstood, Jeraly.)

Of course, any solution involves smaller pens. These two ideas do mean much smaller pens, but even the accepted solution requires pens less than half the original area.

*EDIT*
Thinking about this further, if we don't assume that the fences are joined at the edges, then the farmer will also need:

Spoiler (Rollover to View):

some means of measuring distances, otherwise he can't ensure the fences are equally-spaced so that the pens are all the same size. He doesn't need one if the fences are just joined at the edges.

Posted: Mon Mar 19, 2007 9:48 am
Last edited by Eugenes Lair on Fri Mar 23, 2007 3:15 pm; edited 2 times in total

rrwoods
Boot

Joined: 07 Feb 2007
Posts: 22

Spoiler (Rollover to View):

Is is also "implied" that the new pens have to be square?

EDIT: Spoilered, since apparently this is a major part of the solve.

Posted: Wed Mar 21, 2007 1:28 pm
Last edited by rrwoods on Wed Mar 21, 2007 2:06 pm; edited 1 time in total

aliendial
Unfictologist

Joined: 29 Sep 2002
Posts: 3438
Location: Far Far Away. Nowhere Near You. Really.

No. That is probably the intended tricky part of the analysis.

_________________
aliendial

Posted: Wed Mar 21, 2007 1:57 pm

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