Sum of the digits

Number Theory Level 2

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

169 99 129 180

Bala Vidyadharan by Bala vidyadharan , 20, India

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2 solutions

Ivan dennys Opit
Jul 4, 2015

9^3=729, sum of its digits 7+2+9=18. 99^2=970299...................... 9 3+7+2= 36= 18(2). 999^3=997002999 9 5+7+2=54=18(3).
so sum of digits from 9999999999 is 18(10)=180

3 Helpful 0 Interesting 0 Brilliant 0 Confused

What about if it would've been 3 in place of 9

Sanjay Malik - 5 years, 11 months ago
Vishal S
Jul 5, 2015

Hi

Solution:

We know that**

9^3=729 => sum of the digits is 18

99^3=970299=>sum of he digits is 36

999^3=997002999=>sum of the digits is 54

From the above, we conclude that

When n.o. of digits in the L.H.S is 1 The the sum of the digits of the resultant is

9 x (2 x n.o of digits in L.H.S)

Since in the question there are 10 digits

Therefore sum of the digit is 9 x (2 x 10)=9 x 20=180

0 Helpful 0 Interesting 0 Brilliant 1 Confused

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