Power digits

Number Theory Level 2

how many digits can have 1000^1000


The answer is 3001.

Aayush Baranwal by AAYUSH BARANWAL , 21, India

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3 solutions

Devansh Shah
Jul 28, 2015

10^3000 = 3000+1 digit = 3001 digits

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Aayush Baranwal
Jul 28, 2015

1000^1000 = (10^3)^1000 = 10^3000 THUS THERE ARE TOTAL 3000 DIGITS (0) BUT HERE WE SEE THERE IS DIGIT 1 IS ALSO PLACED IN THE GIVEN NUMBER. THEREFORE, TOTAL NO. OF DIGITS ARE 3001

1 Helpful 0 Interesting 0 Brilliant 0 Confused

You should change the question to "How many digits are there in 100 0 1000 1000^{1000} " instead of "how many digits can have 100 0 1000 1000^{1000} .

Anuj Shikarkhane - 5 years, 10 months ago

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if i put the question about your then the given question will changed into 1000^1000 x 1000^2000 x 1000^3000 x .......... x 1000^(1000 x n) which is not related to my answer

AAYUSH BARANWAL - 5 years, 7 months ago
Rahul Choudhury
Aug 26, 2015

See,the pattern; an elegant way of solving, Let T 1= 1000---> 4 digits T 2=1000^2--->7 digits; T 3=1000^3---->10 digits. Now,we can clearly,see that number of digits are in AP with common difference 3. So, T 1000=1000^1000=4+999*3=3001

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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