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Lamps in a row (Posted on 2010-09-03) Difficulty: 4 of 5
There are n ≥ 2 lamps L1, L2, ..., Ln in a row. Each of them is
either on or off. Initially L1 is on and all of the others are off.
Each second the state of each lamp changes as follows:

if the lamp and its neighbors (L1 and Ln have one neighbor,
any other lamp has two neighbors) are in the same state,
then it is switched off; otherwise, it is switched on.

Prove or disprove that all of the lamps will eventually be switched off
if and only if n is a power of two.

Note: This is a problem that I modified from one proposed but not used at
the 47th IMO in Slovenia 2006.

No Solution Yet Submitted by Bractals    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
Hints/Tipsfurther thoughtsbroll2010-09-05 06:22:34
some thoughts.broll2010-09-04 16:10:54
re: How problem was modifiedGamer2010-09-04 02:53:27
How problem was modifiedBractals2010-09-04 01:49:20
re(2): Almost proved: two gapsGamer2010-09-03 23:52:40
re: Almost proved: two gapsBractals2010-09-03 20:10:34
Almost proved: two gapsJer2010-09-03 15:34:40
re: questionBractals2010-09-03 14:31:13
Questionquestionbroll2010-09-03 04:22:37
re: solution (half)Gamer2010-09-03 04:17:50
SolutionsolutionDej Mar2010-09-03 04:01:12
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