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Here is one solution for the easy version: solution 1. Start at either one of the top two points.
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I got the hard version. You can see it Here. The top three diagrams are 3 additional solutions to the basic version. The bottom drawing is a solution the hard version. The key, apparently, is that no point has more than one line passing through it. For the 4 solutions I have to the basic version, note that the original solution and the far left solution are variations on the same basic idea while the middle and right solutions are also variations on the same basic idea.
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Great job. My solution to the tough version was basically your top-middle path, where with minor adaptation the path can start on the top right of the inner points.
Not revisiting points is therefore not a requirement for the tough solution, although it would be one hell of an additional constraint. |
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New box to think outside of:
You have a perfect string (no stretch) that's snug around a perfect planet ()no squeeze). You increase the length of the string by 1 inch then pull up. How high off the ground will you lift the string?
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Assuming that you want a uniform height to the string: since you increase the circumference by 1 inch, you can increase the radius by 1/2pi inches. In real units that's 4mm.
Edit to add: On the pull-up to the horizon on an Earth-sized planet I got 413 inches (10.49m), close enough the same as hhEb09'1. Last edited by Joff; 02-May-2006 at 08:35 PM. |