[Paterson's Worms cases] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Paterson's Worms cases
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Posted by: Ed Pegg Jr
Ben Chaffin and Al Zimmermann have resolved three cases of the Paterson Worm problem that have been unsolved since 1971. In addition to page 880 of NKS, the problem is described at http://www.accessv.com/~sven/worms
Worm {2,1,4,5,1,4,2} ends after 87996218 steps.
Worms {2,0,1,4,1,4,2} and {2,4,5,4,1,4,2} end after 3563608205 steps, and wound up making the same pattern, rotated 120 degrees.
Worms {1,4,2,0,2,2,4} and {1,4,5,0,2,2,4} required 16811365528 steps, and made the same pattern, rotated 180 degrees.
Other results are at his webpage, http://wso.williams.edu/~bchaffin/patersons_worms/.
--Ed Pegg Jr
Posted by: Ed Pegg Jr
http://www.maa.org/editorial/mathga...s_10_24_03.html
has a larger explanation, along with Mathematica code.
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