Do it here!

Find the sum of digits of ( 9999999999 ) 3 (9999999999)^3 .


The answer is 180.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rakshit Joshi
Oct 31, 2015

its solution is based on observation 9³ = 729 → 7 + 2 + 9=18 (18*1=18).

99³ = 970299 → 9 + 7 +0 + 2 + 9 + 9=36 (18*2=36).

999³= 997002999→ 9+ 9+ 7+2+9+9+9=54 (18*3=54).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . upto

(9999999999)³= 18*10=180.

Therefore the answer is 180.

Can you explain the observation? How do you know that it holds for 10 digits?

Hint: Consider 999...9 = 1 0 n 1 999 ... 9 = 10^n -1 .

Calvin Lin Staff - 5 years, 7 months ago

Log in to reply

The pattern is :

(999...n times)^3 sum is = 9 2 n

Dev Sharma - 5 years, 7 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...