How many zeros and how many ones are there in the numbers from 1 to 9999? Example: in the number 1010 there are 2 zeros and 2 ones.


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Question Number 53902 by mr W last updated on 27/Jan/19

$H o w m a n y z e r o s a n d h o w m a n y o n e s$ $a r e t h e r e i n t h e n u m b e r s f r o m 1 t o$ $9999 ?$ $E x a m p l e : i n t h e n u m b e r 1010 t h e r e$ $a r e 2 z e r o s a n d 2 o n e s .$
Commented by tanmay.chaudhury50@gmail.com last updated on 27/Jan/19

$s i r e x c e l l e n t q u e s t i i n . . . t r y i n g t o s o l v e . .$ $p l s d o n o t p o s t a n s w e r t i l l t h e g o a l i s r e a c h e d$ $. . . i f n o t s u c c e e d . . . t h e n y o u p l s u p l o a d a n s w e r$
Commented by Tawa1 last updated on 27/Jan/19

$Good question$
Commented by mr W last updated on 27/Jan/19

$i h a v e n o t g o t t h e a n s w e r y e t . p l e a s e$ $t r y t o s o l v e . t h a n k s s i r!$
	Answered by tanmay.chaudhury50@gmail.com last updated on 27/Jan/19

	$c a l c u l a t i o n o f z d r o e s . . .$ $1) o n e d i g i t n o \to u s e o f z e r o \to i s 0 \to 0 ◼$ $2) T w o d i g i t n o \to w h e n u n i t p l a c e \to 0$ $t e n g t h d i g i t c a n b e f i l l e d b y a n y n u m b e r \to (1, 2, 3 . . 9)$ $s o 9 n u m b e r s \to 9 ◼$ $3) T h r e e d i g i t n u m b e r \to u n i t p l a c e \to 0$ $t e n g t h p l a c e c a n b e f i l l e d \to (1, 2, . . . 9) \to 9 w a y s$ $h u n d r e d c a n b e f i l l e d \to (1, 2 . . . 8) 9 w a y s$ $s o t o t a l = 1 \times 9 \times 9 = 81$ $n o w u s e o f 0 i n t h i s 81 n u m b e r s = 81 ◼$ $T h r e e d i g i t n o u n i t p l a c e \to 0$ $[a l s o t e n t h p l a c e \to 0$ $h u n d r e d p l a c e \to c a n b e f i l l e d \to u s i n g (1, 2, 3 . . 9)$ $\to 9 w a y s \to 9 n u m b d r s \to e . g [100, 200, . . 900]$ $u s e o f 0 i n t h i s 9 n u m b e r s = 9 \times 2 = 18 ◼$ $T h r e e d i g i t n o t e n g t h p l a c e 0 \to u n i t p l a c (1 t o 9) \to$ $h u n d r e d p l a c e \to a n y n u m b e r (1, 2, 3 . . 9)$ $9 \times 1 \times 9 = 81$ $u s e o f 0 \to 1 \times 81 = 81 ◼$ $4) f o u r d u g i t n o$ $\overset{\times}{-} \overset{\times}{-} \overset{\times}{-} \overset{0}{-} \to 9 \times 9 \times 9 \times 1 = 729$ $\overset{\times}{-} \overset{\times}{-} \overset{0}{-} \overset{\times}{-} \to 9 \times 9 \times 1 \times 9 = 729$ $\overset{\times}{-} \overset{0}{-} \overset{\times}{-} \overset{\times}{-} \to 9 \times 1 \times 9 \times 9 = 729$ $\overset{\times}{-} \overset{\times}{-} \overset{0}{-} \overset{0}{-} \to 9 \times 9 \times 1 \times 1 = 81$ $\overset{\times}{-} \overset{0}{-} \overset{\times}{-} \overset{0}{-} \to 9 \times 1 \times 9 \times 1 = 81$ $\overset{\times}{-} \overset{0}{-} \overset{0}{-} \overset{\times}{-} \to 9 \times 1 \times 1 \times 9 = 81$ $u s e o f 0 [729 + 729 + 729] \times 1 ◼$ $u s e o f 00 [81 + 81 + 81] \times 2 ◼$ $\overset{\times}{-} \overset{0}{-} \overset{0}{-} \overset{0}{-} \to 9 \times 1 \times 1 \times 1 = 9$ $u s e o f 000 = 9 \times 3 = 27 ◼$ $s i r p l s c h e c k t i l l n o w t o g e t t h e u s e o f 0$ $w e h a v e t o a d d ◼ m a r k e d v a l u e . . .$ $p l s c h e c k . .$ $i h a v e c s l c u l a t e d o n l y u s e o f 0 t i l l n o w . .$
	Commented by mr W last updated on 27/Jan/19

	$c o r r e c t s i r!$
	Commented by Otchere Abdullai last updated on 27/Jan/19

	$B r i l l i a n t$
	Commented by tanmay.chaudhury50@gmail.com last updated on 28/Jan/19

	$t h a n k y o u s i r f o r y o u r k i n d p e r u s a l t h r o u g h i t . .$ $n o w i s h a l l t r y t o s o l v e f o r 1 . . .$
	Commented by Tawa1 last updated on 28/Jan/19

	$God bless you sir$
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