## Conundrum I : Help Varun!

**Varun and Rahul sit together, Rahul asks varun find the sum of the sum of the digits of all natural numbers upto 10. Varun quickly answers 46. Rahul again asks what if we find upto 50, varun takes some time and answers 330. Rahul stands up and says, Can you find it for 2008, and do it before I count upto 20?**

*Your task is to help Varun, How will you do that?*

hi varun,,,,,grt qust………

i tried ..my ans is 18054

my funda…(20*900)+54=18054

900=sum of sum of digit for 1-99,100-199,200-299,….1900-1999.

54=sum of sum of digit for 2000-2008

vishal agrawalAugust 28, 2008 at 7:04 pm

good attempt!! but a counting error

try again !!

outtimedAugust 28, 2008 at 7:28 pm

wr is the mistake……

vishal agrawalAugust 28, 2008 at 8:04 pm

you have not counted for the hundreds digit and thousands digit

outtimedAugust 28, 2008 at 9:14 pm

plz solve……….

vishal agrawalAugust 31, 2008 at 7:10 pm

Method 1: 100(9+10+..18 ) + 100(10+11+…+19) +54 = 28054

Method 2: 4.5*3*1000 + (4.5*3*1000+1000) +54 =28054

Vineet SinghSeptember 1, 2008 at 6:12 pm

Breaking the numbers till 2008 into 4 parts:

Units digit can have numbers from 1-9 for 200 times.

Same for tens and hundreds digits.

=45*(200+200+200)

Now, for numbers from 1000 to 1999, 1 is there 1000 times.

and adding digits of numbers 2000-2008.

We get, 27000+1000+9*2+36=28054

MilindSeptember 1, 2008 at 6:25 pm

Hey.. I couldnt understand the question itself.. can somebody plzzzzzzzzz explain it to me in detail……… what do u mean by sum of sum of digits..?? n if what i understood was true .. how cud it be 46 for those upto 10??? plzz reply.. its eating my brains out…

VamsiSeptember 7, 2008 at 7:09 am

well done vineet and milind

milind has solved exactly in the way i did

outtimedSeptember 11, 2008 at 12:48 pm

when u say sum of the sum of the digits.. it can be interpreted this way as well right?

sum of the digits from one to ten is 55.

sum of the digits of (sum of the digits ) is= 5+5=10.

since its given as 45, we know they mean that its 1+2+3+4…1+0(upto ten) but the actual meanin can be taken as what i have mentioned right? someone please clarify!!

SamJuly 20, 2009 at 8:21 am

we have to find the sum of the sum of digits of all numbers

it means say a number is n

we find its sum of digits say s(n)

now we sum all s(n) from n=1 to 2008

RahulJuly 23, 2009 at 8:07 am