A-0-1-2-3-2020-how-many-zero-on-A-

Question Number 95846 by naka3546 last updated on 28/May/20

A = {0, 1, 2, 3, \dots, 2020}

h o w m a n y z e r o o n A ?

Answered by Rasheed.Sindhi last updated on 28/May/20

^{'}_^{'} is nonzero digit in the following .

1 - digit numbers :

0 : 1 \times 1 = 1 (1 z e r o)

2 - digit numbers :

_0 : 9 \times 1 = 9

3 - digit numbers :

__0 : 9 \times 9 \times 1 = 81 \times 1 = 81

_0_: 9 \times 1 \times 9 = 81 \times 1 = 81

_00 : 9 \times 1 \times 1 = 9 \times 2 = 18

4 - digit numbers :

S i n g l e z e r o

1__0 : 1 \times 9 \times 9 \times 1 = 81

1_0_: 1 \times 9 \times 1 \times 9 = 81

10__: 1 \times 1 \times 9 \times 9 = 81

2__0 : 1 \times 0 \times 2 \times 1 = 0

2_0_: 1 \times 0 \times 1 \times 9 = 0

20 1_: 1 \times 1 \times 1 \times 9 = 9

202_: 1 \times 1 \times 1 \times 0 = 0

{81 \times 3 + 9} \times 1 = 252

D o u b l e z e r o s

10_0 : 1 \times 1 \times 9 \times 1 = 9

10 0_: 1 \times 1 \times 1 \times 9 = 9

1_00 : 1 \times 9 \times 1 \times 1 = 9

20_0 : 1 \times 1 \times 2 \times 1 = 2

20 0_: 1 \times 1 \times 1 \times 9 = 9

2_00 : 2 \times 0 \times 1 \times 1 = 0

(9 \times 4 + 2) \times 2 = 76

T r i p l e z e r o s

1000 : = 1 \times 3 = 3

2000 : = 1 \times 3 = 3

6

A n s w e r : 524

P l e a s e c o n f i r m .

Commented by naka3546 last updated on 22/Jun/20

T h a n k y o u, s i r . {I t}^{'} s c o r r e c t .

Commented by Rasheed.Sindhi last updated on 22/Jun/20

{Y o u}^{'} r e w e l c o m e s i r!