Question Number 208071 by hardmath last updated on 03/Jun/24
$$\frac{\mathrm{4}\:\centerdot\:\mathrm{10}^{\boldsymbol{\mathrm{n}}} \:−\:\mathrm{52}}{\mathrm{3}} \\ $$$$\mathrm{The}\:\mathrm{numbers}\:\mathrm{are}\:\:\mathrm{38}\:\:\mathrm{in}\:\mathrm{total} \\ $$$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{n}}\:=\:? \\ $$
Commented by mr W last updated on 04/Jun/24
$${it}'{s}\:{not}\:{clear}\:{what}\:{you}\:{mean}. \\ $$
Commented by hardmath last updated on 04/Jun/24
$$\mathrm{dear}\:\mathrm{professor},\:\mathrm{answer}:\:\mathrm{12} \\ $$
Commented by mr W last updated on 04/Jun/24
$${how}\:{is}\:{an}\:{answer}\:{possible},\:{if}\:{it}\:{is} \\ $$$${not}\:{clear}\:{what}\:{the}\:{question}\:{is}? \\ $$
Commented by TonyCWX08 last updated on 04/Jun/24
$${Since}\:{you}\:{have}\:{the}\:{answer},\:{why}\:{are}\:{you}\:{here}? \\ $$
Commented by Frix last updated on 04/Jun/24
$$\mathrm{Maybe}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{38}? \\ $$$$\mathrm{In}\:\mathrm{this}\:\mathrm{case}: \\ $$$${n}\:\:\:\:\:\mathrm{Sum}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{of}\:\frac{\mathrm{4}×\mathrm{10}^{{n}} −\mathrm{52}}{\mathrm{3}} \\ $$$$\mathrm{2}\:\:\:\:\:\:\mathrm{1}+\mathrm{1}+\mathrm{6} \\ $$$$\mathrm{3}\:\:\:\:\:\:\mathrm{1}+\mathrm{3}+\mathrm{1}+\mathrm{6} \\ $$$$\mathrm{4}\:\:\:\:\:\:\mathrm{1}+\mathrm{3}+\mathrm{3}+\mathrm{1}+\mathrm{6} \\ $$$${n}\:\:\:\:\:\:\mathrm{1}+\left({n}−\mathrm{2}\right)×\mathrm{3}+\mathrm{1}+\mathrm{6}=\mathrm{3}{n}+\mathrm{2} \\ $$$$\mathrm{3}{n}+\mathrm{2}=\mathrm{38} \\ $$$${n}=\mathrm{12} \\ $$$$\frac{\mathrm{4}×\mathrm{10}^{\mathrm{12}} −\mathrm{52}}{\mathrm{3}}=\underset{\mathrm{Sum}=\mathrm{38}} {\underbrace{\mathrm{1}\:\mathrm{333}\:\mathrm{333}\:\mathrm{333}\:\mathrm{316}}} \\ $$
Commented by hardmath last updated on 04/Jun/24
$$\mathrm{yes}\:\mathrm{professor} \\ $$