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