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Question Number 51465 by mr W last updated on 27/Dec/18

Commented by Rasheed.Sindhi last updated on 27/Dec/18

$S i r 4 - d i g i t n u m b e r s I t h i n k ?$
Commented by mr W last updated on 27/Dec/18

$Y e s, 4 - d i g i t s n u m b e r s o n l y .$
Commented by Rasheed.Sindhi last updated on 27/Dec/18

$711040 ?$
Commented by mr W last updated on 27/Dec/18

$c o r r e c t! t h a n k y o u s i r!$
	Answered by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18

	$t o t a l f o u r d i g i t n u m b e r s f o r m e d = 4 \times 4 \times 4 \times 4 = 256$ $d u r i n g a d d i t i o n$ $w e h a v e t o a d d e a c h d i g i t 64 t i m e s .$ $1) s o u n i t p l a c e o f t h e s u m o f a l l f o u r d i g i t i s$ $[64 \times (1 + 2 + 3 + 4) = 640] \to 0$ $2) w h e n w e a d d a l l d i g i t o f s e c o n d p l a c e + c a r r y$ $f o r w a r d 64 [640 + 64 = 704] s o t e n t h d i g i t o f s u m \to 4$ $3) h u n d r e d p l a c e [640 + 70 = 710] \to 0$ $4) t h o u s a n d p l a c e [640 + 71 = 711] \to 1$ $s o a n s w e r i s 711040$
	Commented by mr W last updated on 27/Dec/18

	$a n s w e r i s c o r r e c t s i r \cdot t h a n k y o u!$
	Answered by mr W last updated on 27/Dec/18

	$s u m o f a l l p o s s i b l e n u m b e r s i s e q u a l$ $t o t h e s u m o f a l l v a l u e s w h i c h t h e i r$ $d i g i t s r e p r e s e n t :$ $\frac{4^{4}}{4} \times (1000 + 100 + 10 + 1) \times (1 + 2 + 3 + 4)$ $= \frac{4^{4}}{4} \times 1111 \times 10 = 711040$
	Commented by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18

	$u n i q u e m e t h o d . . . e x c e l l e n t . . .$
	Commented by ajfour last updated on 27/Dec/18

	$s t a n d a r d o l d m e t h o d . .$
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