Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspxI find people will often say something is impossible, when really they just aren't s mart enough to figure it out.
Physicists (and the Discovery channel) love pointing this out about time-travel: No law of physics, except for perhaps the law abouten-USTelligent Evolution Platform Developer Build (Build: 5.6.50428.7875)Number puzzlehttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#3252173Tue, 12 Jun 2007 19:04:33 GMT91d46819-8472-40ad-a661-2c78acb4018c:3252173Mike Stall's .NET Debugging Blog<p>Here's a little number puzzle quiz. Fill in the digits: ABC + DEF GHI Where each letter represents a</p>
<img src="http://blogs.msdn.com/aggbug.aspx?PostID=3252173" width="1" height="1">Living with the consequences.http://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#529962Sat, 11 Feb 2006 03:39:27 GMT91d46819-8472-40ad-a661-2c78acb4018c:529962Mike Stall's .NET Debugging BlogSometimes we think we can make a decision, but it turns out the decision is already made for us by the...<img src="http://blogs.msdn.com/aggbug.aspx?PostID=529962" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#527165Wed, 08 Feb 2006 04:12:35 GMT91d46819-8472-40ad-a661-2c78acb4018c:527165Been through too many "paradigms"The real answer is 0.
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<br />You're missing the obvious solution, like the Microsoft solution in coming out with C# on .NET to replace C++ -- just mash that square into on little blob and you don't need any darn wire.<div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=527165" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#526468Tue, 07 Feb 2006 13:15:55 GMT91d46819-8472-40ad-a661-2c78acb4018c:526468Barry.Kellydimkaz: I see no proof in Roger's entry. It talks about ones next "impulse", and then splits the point in two, and then asserts that "this is the best steiner tree for the square".
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<br />My only goal was to prove that "C" wasn't the most optimal entry, and I did by providing an example that was better than it.<div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=526468" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#526179Tue, 07 Feb 2006 03:56:49 GMT91d46819-8472-40ad-a661-2c78acb4018c:526179SteveJSCool ... Steiner points. :-)
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<br />I remember a somewhat similar problem in a freshman college course on tricky Math problems.
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<br />Rather than connect all the points, you must instead prevent any line from intersecting 2 edges without intersecting at least one line segment interior to the square. Obviously the solution to the problem above satisfies the condition. But is there a better one that uses line segments of less total length?
<br /><div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=526179" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#526158Tue, 07 Feb 2006 03:21:45 GMT91d46819-8472-40ad-a661-2c78acb4018c:526158Roger WolffDavid,
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<br />Yeah, my high school geometry teacher did a pretty neat demo for us. He brought in two parallel pieces of plastic, connected by metal rods at the vertices. He dipped the contraption into a bucket of soapy water, and voila! -- steiner points.<div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=526158" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#525954Mon, 06 Feb 2006 23:21:56 GMT91d46819-8472-40ad-a661-2c78acb4018c:525954Mike Stall - MSFTRoger - you're a step ahead of me. :)
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<br />I didn't want to come out and say "C" was the wrong answer because that would give things away. It's very interesting to see somebody passionately "proove" that C is correct. Since C is not correct, their proof will obviously be wrong. So at what point does the lightbulb go on that "I can't proove C is correct, so maybe C is incorrect and their is actually a better way".
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<br />I guess if I had thought ahead, I would have moderated the comments so that nobody would give away the answer. Alas, maybe next time :)
<br /><div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=525954" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#525939Mon, 06 Feb 2006 22:47:03 GMT91d46819-8472-40ad-a661-2c78acb4018c:525939David SrbeckyIsn't this the kind of shape you get if you play with soap in the bathroom? :-)<div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=525939" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#525874Mon, 06 Feb 2006 21:33:14 GMT91d46819-8472-40ad-a661-2c78acb4018c:525874dimkazClearly you need "the theory".
<br />You assumed (and didn't prove) that "H" shape is the best.
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<br /><div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=525874" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#525859Mon, 06 Feb 2006 21:24:53 GMT91d46819-8472-40ad-a661-2c78acb4018c:525859Barry.KellyI see Roger has gotten ahead of me, but I needed to work it out without the help of the theory.
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<br />I wrote an equation that described the total wire length when using a "squeezed H", with an adjustable "waist", length x:
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<br />x + 4 * sqrt((1 - 2*x + x*x)/4 + 1/4)
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<br />Using a test value for x of 0.5 (trying to neutralize the 1 with 2*0.5, yet knowing that x*x < x for 0 < x < 1. Using x as 0.5, the total wire length is:
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<br />2.7360679774997896964091736687313
<br /><div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=525859" width="1" height="1">re: Impossible vs. Insufficiently Cleverhttp://blogs.msdn.com/b/jmstall/archive/2006/02/06/impossible-vs-insufficiently-clever.aspx#525843Mon, 06 Feb 2006 21:10:44 GMT91d46819-8472-40ad-a661-2c78acb4018c:525843Roger WolffLookup steiner points. The shortest distance is, according to the link below, 2.732.
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<br /><a rel="nofollow" target="_new" href="http://www.mathreference.com/gph,stein.html">http://www.mathreference.com/gph,stein.html</a>
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<br />"Let's connect the corners of a unit square. Without steiner points, the spanning tree has length 3, with 3 of the 4 sides drawn in. Your next impulse is to connect the four corners to the center, introducing one steiner point. This gives an edge length of 2.828, a definite improvement over 3. Next, split the steiner point in two and pull the two points apart, towards the left and right sides of the square, until the angles are 120°. This gives an edge length of 2.732. This is the best steiner tree for the square."<div style="clear:both;"></div><img src="http://blogs.msdn.com/aggbug.aspx?PostID=525843" width="1" height="1">