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-

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 \dots 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

\dots i f n o t s u c c e e d \dots 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 \dots

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, \dots 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 \dots 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 \dots

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 \dots

Commented by Tawa1 last updated on 28/Jan/19

God bless you sir

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