December 2008
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Consider a random walk on the 2-d integer lattice starting at (0,0). From a lattice point (i,j) the walk moves to one of the four points (i-1, j), (i+1, j), (i, j-1) or (i, j+1) with equal probability. The walk continues until four different points (including (0,0)) have been visited. These four points will form one of the five tetrominoes (considering mirror images to be the same). For each tetromino find the probability that it will be the one formed in this way.
Please make sure you clearly identify the tetrominoes when submitting a solution. You may wish to use the wikipedia letter designations, I,L,O,S and T. A few solutions did not receive credit
because I could not tell which tetrominoes were which. Also I am requiring exact values for the probabilities.
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Challenge:
12/01/2008 @ 05:30 PM EST
Solution:
01/01/2009 @ 05:30 PM EST
List Updated:
12/31/2008 @ 08:00 AM EST
People who answered correctly:
Andreas Kabel (12.02.2008 @03:48 AM EST)
Kenneth Arnold (12.02.2008 @05:08 AM EST)
Leo Broukhis (12.02.2008 @10:49 PM EST)
Anneke van Steirteghem (12.02.2008 @10:59 AM EST)
Dario Serino (12.02.2008 @11:15 AM EST)
Bob English (12.02.2008 @12:03 AM EST)
Jonathan Campbell (12.02.2008 @01:56 AM EST)
Jack Kennedy (12.02.2008 @02:35 AM EST)
Richard Bjorklund and Carl Hammarlund (12.02.2008 @03:00 AM EST)
Michel Speiser (12.02.2008 @07:40 AM EST)
Arthur Brietman (12.02.2008 @01:30 PM EST)
Alexander Belton (12.02.2008 @02:14 PM EST)
Alex Wagner (12.02.2008 @02:49 PM EST)
Mark Perkins (12.02.2008 @03:03 PM EST)
Michael Schaaf (12.02.2008 @04:07 PM EST)
V Balakrishnan (12.02.2008 @05:19 PM EST)
James Riordan (12.02.2008 @05:28 PM EST)
Xiaoyang Guan (12.02.2008 @06:01 PM EST)
Maris van Sprang (12.02.2008 @06:43 PM EST)
Andreas Eisele (12.02.2008 @07:05 PM EST)
Reinder Verlinde (12.02.2008 @07:42 PM EST)
Michael Liepelt (12.02.2008 @07:45 PM EST)
Adam Swejk (12.02.2008 @08:21 PM EST)
Michael Traut (12.02.2008 @08:46 PM EST)
Aditya K Prasad (12.03.2008 @12:18 AM EST)
Gary M. Gerkin (12.03.2008 @03:25 AM EST)
Jesse Kolman (12.03.2008 @03:41 AM EST)
John Ritson (12.03.2008 @03:50 AM EST)
Joe Riel (12.03.2008 @03:55 AM EST)
John T. Robinson (12.03.2008 @05:42 AM EST)
Christian Blatter (12.03.2008 @06:53 AM EST)
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Ben Tarlow (12.03.2008 @02:29 PM EST)
James Dow Allen (12.04.2008 @05:49 AM EST)
Harold Gutch (12.04.2008 @11:08 AM EST)
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Dan Dima (12.04.2008 @12:03 PM EST)
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Caltech Math Students (12.05.2008 @12:53 PM EST)
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Nyles Heise (12.08.2008 @07:00 AM EST)
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Ross Millikan (12.08.2008 @02:54 PM EST)
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Dave Parashar (12.10.2008 @02:23 AM EST)
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Chris French (12.10.2008 @07:27 PM EST)
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Al Zimmermann (12.11.2008 @09:53 PM EST)
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Uri Yanover (12.12.2008 @06:50 AM EST)
Anton Luht (12.12.2008 @11:09 AM EST)
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Niraj Jha (12.14.2008 @04:26 PM EST)
Rickey Bowers (12.15.2008 @07:05 AM EST)
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Martin Giese (12.15.2008 @09:28 PM EST)
Adam Daire (12.16.2008 @02:23 AM EST)
Hui Wang (12.16.2008 @05:11 AM EST)
Ian Smith (12.17.2008 @11:51 AM EST)
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Reiner Martin (12.31.2008 @05:22 PM EST)
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