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IMO Shortlist 2005 C1
Posted: Tue May 21, 2013 7:57 am
by Phlembac Adib Hasan
A house has an even number of lamps distributed among its rooms in such a way that there are at least three lamps in every room. Each lamp shares a switch with exactly one other lamp, not necessarily from the same room. Each change in the switch shared by two lamps changes their states simultaneously. Prove that for every initial state of the lamps there exists a sequence of changes in some of the switches at the end of which each room contains lamps which are on as well as lamps which are off.
Proposed by Australia
Re: IMO Shortlist 2005 C1
Posted: Mon Mar 31, 2014 10:44 pm
by asif e elahi
Phlembac Adib Hasan wrote:A house has an even number of lamps distributed among its rooms in such a way that there are at least three lamps in every room. Each lamp shares a switch with exactly one other lamp, not necessarily from the same room. Each change in the switch shared by two lamps changes their states simultaneously. Prove that for every initial state of the lamps there exists a sequence of changes in some of the switches at the end of which each room contains lamps which are on as well as lamps which are off.
Proposed by Australia
I don't understand the problem.Please convert it in Bengali.