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In-each-square-of-a-5-5-board-there-is-a-lamp-turned-off-If-we-touch-a-lamp-then-that-lamp-and-the-ones-in-neighbouring-squares-the-squares-which-share-a-side-change-their-states-After-a-certain-




Question Number 160269 by Unnamed last updated on 27/Nov/21
In each square of a 5×5 board there  is a lamp turned off.If we touch  a   lamp then that lamp and the ones in   neighbouring squares(the squares   which share a side)change their   states.After a certain number of   moves,Is it possible to turn on all   lamps?Give Reason?
$${In}\:{each}\:{square}\:{of}\:{a}\:\mathrm{5}×\mathrm{5}\:{board}\:{there} \\ $$$${is}\:{a}\:{lamp}\:{turned}\:{off}.{If}\:{we}\:{touch}\:\:{a}\: \\ $$$${lamp}\:{then}\:{that}\:{lamp}\:{and}\:{the}\:{ones}\:{in}\: \\ $$$${neighbouring}\:{squares}\left({the}\:{squares}\:\right. \\ $$$$\left.{which}\:{share}\:{a}\:{side}\right){change}\:{their} \\ $$$$\:{states}.{After}\:{a}\:{certain}\:{number}\:{of}\: \\ $$$${moves},{Is}\:{it}\:{possible}\:{to}\:{turn}\:{on}\:{all}\: \\ $$$${lamps}?{Give}\:{Reason}? \\ $$$$ \\ $$$$ \\ $$
Commented by Rasheed.Sindhi last updated on 27/Nov/21
Except one bulb all can be turned on.  At least according to my solution.
$$\mathcal{E}{xcept}\:{one}\:{bulb}\:{all}\:{can}\:{be}\:{turned}\:{on}. \\ $$$${At}\:{least}\:{according}\:{to}\:{my}\:{solution}. \\ $$

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