On a circle there are 2014 light bulbs, 2 are ON, and 2012 are OFF. You can choose any bulb and change the neighbor's state from ON to OFF or from OFF to ON. Doing so, can we get all 2014 light bulbs on ? If yes, How?

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On a circle there are 2014 light bulbs, 2 are ON, and 2012 are OFF. You can choose any bulb and change the neighbor's state from ON to OFF or from OFF to ON. Doing so, can we get all 2014 light bulbs on ? If yes, How?

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yes, it is possible. Keeping two lighted bulbs adjacent.

Let's assume initial state of circuit as {0,0,0,1,1,0,0,0,0.....,0,0}

where 1 = Switched ON nd 0 = Switched OFF

choose second last bulb from bulb which has state =1, then 2 bulb will be lighted on either sides

next state becomes {1,0,1,1,1,1,0,1,0,0,0.....0,0}

so at each step we are lighting 4 bulbs, since 2012 is multiple of 4, there will come a stage where all bulbs will be ON.

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