Question

let S be the sum of all digits used in writing all numbers from 1 to 1010. the sum of digits of S is

Answer 1

it doesnt even form an AP .:(

Answer 2

do it step by step, slowly

Answer 3

but how adding dem all .?

Answer 4

00-09 = sum9
10-19 = 1*10 + sum9
20-29 = 2*10 + sum9
...
90-99 = 9*10 + sum9
----------------------
10*sum9 + 10(sum 9)
sum9(20) = 45*20 = 900

so 00->99 the sum of digits used is 900

Answer 5

alright .!

Answer 6

btw, sum9 = 0+1+2+3 + .... 9

Answer 7

next, consider 100->999

100->199 = 1*100 + 900
200->199 = 2*100 + 900
....

Answer 8

yeah ..i interpreted .!

Answer 9

for 100->999 :
if you add them all, clearly u wud get :-
100(sum9) + 10*900

Answer 10

4500+9000=13500

Answer 11

dont forget to add 00->99
and 1000->1010

:)

Answer 12

I was lazy and did it with Mathematica and got 13,501

Answer 13

65+900 also to be included .!

Answer 14

something is incorrect ..in my work .??

Answer 15

mathematica cannot be wrong.
lets work it wid more attention :)


we made a mistake, corrected below :-
for 100->999 :
if you add them all, clearly u wud get :-
100(sum9) + \(\color{red}{9} \)*900

Answer 16

100 - 999, there are 9 groups of 100s. not 10.

Answer 17

ohh ..yes//

Answer 18

Here is the Mathematica Code to do it
Total[Table[Total[IntegerDigits[j]], {j, 1, 1000}]]

Answer 19

what is that ..voo .?

Answer 20

ahh we're right !
we also got 13501 for the numbers between 1 & 1000

Answer 21

then ...for 1010 also right .? .!

Answer 22

00->99 : 900
100->999 : 100(sum9) + 9*900 = 4500 + 8100 = 12600
1000->1010 : 1*11 + sum9 + 1 = 12 + 45 = 57

add them

Answer 23

S=13557
so the sum of digits of S is 21 ..yeah ..
a medal was the least honor to u ..! thank u .! sir @ganeshie8
and @eliassaab ..for correcting that

Answer 24

np :)

Answer 25

Mathematica agrees
Total[Table[Total[IntegerDigits[j]], {j, 1, 1010}]] = 13557

Answer 26

actually ..some script problem ..i am not being able to see in the desired format ..! ..but is that ..any direct formula to do that .?

Answer 27

I am thinking about it

Answer 28

Your problem can be found on
http://answers.yahoo.com/question/index?qid=20100327133907AAp8Umm
One of the solution is similar to what you did above

Answer 29

ohh ..yes ..