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Platform Puzzle #1088 by Bram
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PuzzleScott



Joined: 30/05/2011 23:06:44
Messages: 21
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Number: Puzzle #1088
Genre: Platform
Author: Bram
Appeared at: April 20, 2009
I think I found a solution to this puzzle that's different from the Revealed solution. I write c, p, s for chain, post, shelf, and - for empty:
c--c--cc
sss---s
-c-----c
-s-ssss
-cpp--c-
-sss-s-
----pp--
Am I missing something? Is this not a valid solution? Thanks.
connect4


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Joined: 04/03/2008 05:04:39
Messages: 246
Location: USA
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The way I've learned this genre, the concept is that you have to place one platform/shelf at a time to build it, with each shelf remaining stable the rest of the time. This seems to require that once you get a shelf in there, you can't use any supporting elements for future shelves.

In your solution, look at the leftmost platform in the 5 row. Its chain is supporting the shelf underneath it, and that shelf has a post that is supporting itself. Thus, I think this is a paradox in the puzzle type, and can't work here.
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HappyDog



Joined: 11/11/2015 18:26:16
Messages: 52
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I, too, am having real difficulty with this puzzle. Either there is something wrong with the solution (which I've not looked at yet) or there is some confusion/ambiguity in the rules.

I have put my working here: http://pasteboard.co/QvN5z4MIM.jpg

As far as I can see, at each stage I am adding fully-supported shelves, and the right number of elements are used in the final solution. However it is still being reported as incorrect.

What am I misunderstanding here?
connect4


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Joined: 04/03/2008 05:04:39
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Location: USA
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From my understanding, that middle row platform on the left is the problem. Long story short, the right end of that platform is supported by the bottom platform underneath it. The left end of the platform below it is supported... by the middle platform. Therefore, you've got an instability that doesn't work.

My explanation probably doesn't make a ton of sense, and I'm not somewhere right now where I can post pics, but that's the gist of this one.
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HappyDog



Joined: 11/11/2015 18:26:16
Messages: 52
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connect4 wrote:
From my understanding, that middle row platform on the left is the problem. Long story short, the right end of that platform is supported by the bottom platform underneath it. The left end of the platform below it is supported... by the middle platform. Therefore, you've got an instability that doesn't work.

My explanation probably doesn't make a ton of sense, and I'm not somewhere right now where I can post pics, but that's the gist of this one. 


I understand what you're describing, I think, but I don't see why it is disallowed.

In my solution, I don't see anything about the way the middle-left shelf is attached on the left that is different from the way the middle-right shelf is attached on the right or the top-right shelf is attached on the right.

What is the rule that forbids the left-hand attachment but allows the two right-hand attachments?
JHe



Joined: 01/12/2011 11:39:39
Messages: 89
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I looked at your pic and indeed it's stable. But it seems that the problem is this rule:
A chain can be used to attach a shelf to the shelf above, provided that that one is already stable, or to the ceiling.

So, you can't slip the last shelf between the existing chains.
HappyDog



Joined: 11/11/2015 18:26:16
Messages: 52
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I don't really see how you derive that conclusion from the rule you posted.

There is nothing to say a shelf can't be attached to an existing chain. If that is the implication, then this needs to be spelt out in the rules, somehow, as it has clearly caused a few people some confusion.

It also implies that it would be invalid to add the top-right shelf after the one below it, but that it is OK to add it before, even though the end result is the same. Given that the puzzle solution is a static snapshot of the final shelf arrangement, I'm not sure how the placement order can reasonably be taken into account.
Shvegait



Joined: 13/02/2010 03:36:12
Messages: 100
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I think the problem is that you are treating the 2-long chain piece on the left as going "through" the small shelf in the middle-left. But the chains don't go "through" shelves. You have to treat the top chain piece as connecting the middle shelf to the stable shelf above it, and then the bottom chain piece is connecting the longer shelf at the bottom to the small middle shelf, NOT the top shelf. The problem is, in this situation, neither the small middle shelf nor the longer bottom shelf is stable, as they rely on each other.

In your 3rd image, you can clearly see that all the shelves are stable, including the longer one in the bottom row. But when you add that extra shelf in the middle-left in the 4th image, you are splitting the chain of length 2 into two smaller chains each of length 1, and you have to treat those chains independently. This creates the situation in which two shelves not known to be stable rely on each other, which violates the rule that each shelf must connect only to the floor, ceiling, or other stable shelves.

Given that the puzzle solution is a static snapshot of the final shelf arrangement, I'm not sure how the placement order can reasonably be taken into account. 

Ironically, this is what led to your confusion here, as you assumed the bottom long shelf was placed before the small middle one. In fact, placement order does not matter, and you should be able to prove, with only the final solution, that each shelf is stable independently, connecting either to only the floor and/or ceiling, or to other shelves you have proved are stable. Hope this helps!
HappyDog



Joined: 11/11/2015 18:26:16
Messages: 52
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Thanks for all your replies. It's not completely intuitive, but I think I've got it now.

Here's what helped me solve it: Imagine that each chain is a down arrow and each post is an up arrow, and each shelf is an arrow that goes both left and right; A correct solution must not contain any loops.

Does that sound right?
Shvegait



Joined: 13/02/2010 03:36:12
Messages: 100
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Yes, exactly! If you think of the shelves, ceiling(s) and floor(s) as nodes in a graph, the chains as down arrows, and the posts as up arrows, then the collection of all of them must form a directed acyclic multigraph, in which each shelf is pointed to by exactly two edges (either from two different nodes, or the same node twice). OK, maybe that's not the most intuitive way to think about it, but it's exactly as you said: treat it like a graph and ensure there are no loops.
HappyDog



Joined: 11/11/2015 18:26:16
Messages: 52
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Could something be added to the puzzle description along these lines, to help future puzzlers? I doubt they'll find this discussion and something a bit more concrete would definitely help.
Tom



Joined: 11/02/2011 01:51:54
Messages: 8
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Many thanks for this discussion - I've been struggling with this genre for years, but now finally understand why I was finding multiple "correct" solutions!!
 
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