Question Number 51465 by mr W last updated on 27/Dec/18
Commented by Rasheed.Sindhi last updated on 27/Dec/18
$${Sir}\:\mathrm{4}-{digit}\:{numbers}\:{I}\:{think}? \\ $$
Commented by mr W last updated on 27/Dec/18
$${Yes},\:\mathrm{4}−{digits}\:{numbers}\:{only}. \\ $$
Commented by Rasheed.Sindhi last updated on 27/Dec/18
$$\mathrm{711040}? \\ $$
Commented by mr W last updated on 27/Dec/18
$${correct}!\:{thank}\:{you}\:{sir}! \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18
![total four digit numbers formed=4×4×4×4=256 during addition we have to add each digit 64 times. 1)so unit place of the sum of all four digit is [64×(1+2+3+4)=640]→0 2)when we add all digit of second place +carry forward 64 [640+64=704] so tenth digit of sum→4 3)hundred place [640+70=710]→0 4)thousand place [640+71=711]→1 so answer is 711040](https://www.tinkutara.com/question/Q51476.png)
$${total}\:{four}\:{digit}\:{numbers}\:{formed}=\mathrm{4}×\mathrm{4}×\mathrm{4}×\mathrm{4}=\mathrm{256} \\ $$$${during}\:{addition} \\ $$$${we}\:{have}\:{to}\:{add}\:{each}\:{digit}\:\mathrm{64}\:{times}. \\ $$$$\left.\mathrm{1}\right){so}\:{unit}\:{place}\:{of}\:{the}\:{sum}\:{of}\:{all}\:{four}\:{digit}\:{is} \\ $$$$\left[\mathrm{64}×\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}\right)=\mathrm{640}\right]\rightarrow\mathrm{0} \\ $$$$\left.\mathrm{2}\right){when}\:{we}\:{add}\:{all}\:{digit}\:{of}\:{second}\:{place}\:+{carry} \\ $$$${forward}\:\mathrm{64}\:\left[\mathrm{640}+\mathrm{64}=\mathrm{704}\right]\:{so}\:{tenth}\:{digit}\:{of}\:{sum}\rightarrow\mathrm{4} \\ $$$$\left.\mathrm{3}\right){hundred}\:{place}\:\left[\mathrm{640}+\mathrm{70}=\mathrm{710}\right]\rightarrow\mathrm{0} \\ $$$$\left.\mathrm{4}\right){thousand}\:{place}\:\left[\mathrm{640}+\mathrm{71}=\mathrm{711}\right]\rightarrow\mathrm{1} \\ $$$${so}\:{answer}\:{is}\:\mathrm{711040} \\ $$$$ \\ $$
Commented by mr W last updated on 27/Dec/18
$${answer}\:{is}\:{correct}\:{sir}\centerdot\:{thank}\:{you}! \\ $$
Answered by mr W last updated on 27/Dec/18
$${sum}\:{of}\:{all}\:{possible}\:{numbers}\:{is}\:{equal} \\ $$$${to}\:{the}\:{sum}\:{of}\:{all}\:{values}\:{which}\:{their} \\ $$$${digits}\:{represent}: \\ $$$$\frac{\mathrm{4}^{\mathrm{4}} }{\mathrm{4}}×\left(\mathrm{1000}+\mathrm{100}+\mathrm{10}+\mathrm{1}\right)×\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}\right) \\ $$$$=\frac{\mathrm{4}^{\mathrm{4}} }{\mathrm{4}}×\mathrm{1111}×\mathrm{10}=\mathrm{711040} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18
$${unique}\:{method}…{excellent}… \\ $$
Commented by ajfour last updated on 27/Dec/18
$${standard}\:{old}\:{method}.. \\ $$