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At Fault Coverage (Posted on 2007-03-22) Difficulty: 3 of 5
Show that a 6x6 square tiled with dominoes will always have at least one fault line.

  Submitted by Brian Smith    
Rating: 2.0000 (1 votes)
Solution: (Hide)
There are 10 possible fault lines in a 6x6 square. If there are no fault lines, each potential fault line must have an even number of dominoes straddling it. Since only 18 dominoes are used to cover a 6x6 square and 20 are needed to straddle all the fault lines, there must be a fault line somewhere in the 6x6 square.

Joel provides a similar solution here.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: A counting solutionSteve Herman2007-03-23 22:43:06
program for the listCharlie2007-03-23 11:32:10
...through the most grievous faultsCharlie2007-03-23 11:29:02
re: all the faultsCharlie2007-03-23 11:27:21
all the faultsCharlie2007-03-23 11:25:31
re: A counting solutionJer2007-03-23 10:46:44
SolutionA counting solutionJoel2007-03-23 03:26:26
re: brute forceCharlie2007-03-22 22:07:09
Solutionbrute forceCharlie2007-03-22 21:57:05
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