- Thread starter
- #1

#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

Given $log_{10} 3=0.4771$

All the digits sum of X =A

All the digits sum of A =B

All the digits sum of B =C

please find C

- Thread starter Albert
- Start date

- Thread starter
- #1

- Jan 25, 2013

- 1,225

Given $log_{10} 3=0.4771$

All the digits sum of X =A

All the digits sum of A =B

All the digits sum of B =C

please find C

- Mar 31, 2013

- 1,309

this is 4771 digits so A < 4771 * 9 or A < 50000

Given $log_{10} 3=0.4771$

All the digits sum of X =A

All the digits sum of A =B

All the digits sum of B =C

please find C

B < 41 so C <= 12 ( if b were 39)

X mod 9 = C mod 9

ax x mod 9 = 0 so C= 0 or 9 as it cannot be 18

as C cannot be zero it is 9

- Thread starter
- #3

- Jan 25, 2013

- 1,225

the answer is correct ,but X is not 4771 digitsthis is 4771 digits so A < 4771 * 9 or A < 50000

B < 41 so C <= 12 ( if b were 39)

X mod 9 = C mod 9

ax x mod 9 = 0 so C= 0 or 9 as it cannot be 18

as C cannot be zero it is 9

- Mar 31, 2013

- 1,309

Thanksthe answer is correct ,but X is not 4771 digits

it is my mistake x is 4772 digits

- Thread starter
- #5

- Jan 25, 2013

- 1,225

B < 41 so C <= 12

here the range of A,B,and C should be edited

(the range of A,B,and C are not correct)

- Mar 31, 2013

- 1,309

so I replace it with correct solution

B < 41 so C <= 12

here the range of A,B,and C should be edited

(the range of A,B,and C are not correct)

A < 4772 * 9 or < 47720 or < 50000

I have taken for A to be the worst case. hence A and B range is OK

- Thread starter
- #7

- Jan 25, 2013

- 1,225

A is 5 digits number

$B<5\times 9=45$

B is 2 digits number

$C<2\times 9=18$

I think your range is OK (more rigid )

$B<5\times 9=45$

B is 2 digits number

$C<2\times 9=18$

I think your range is OK (more rigid )

Last edited: