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?


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Question Number 160269 by Unnamed last updated on 27/Nov/21

$I n e a c h s q u a r e o f a 5 \times 5 b o a r d t h e r e$ $i s a l a m p t u r n e d o f f . I f w e t o u c h a$ $l a m p t h e n t h a t l a m p a n d t h e o n e s i n$ $n e i g h b o u r i n g s q u a r e s (t h e s q u a r e s$ $w h i c h s h a r e a s i d e) c h a n g e t h e i r$ $s t a t e s . A f t e r a c e r t a i n n u m b e r o f$ $m o v e s, I s i t p o s s i b l e t o t u r n o n a l l$ $l a m p s ? G i v e R e a s o n ?$
Commented by Rasheed.Sindhi last updated on 27/Nov/21

$E x c e p t o n e b u l b a l l c a n b e t u r n e d o n .$ $A t l e a s t a c c o r d i n g t o m y s o l u t i o n .$
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