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What is smallest 3 digit narcissistic number.


The answer is 153.

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3 solutions

Brock Brown
Mar 17, 2015

Python 2.7:

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def narcissist(n):
    digits = len(str(n))
    return n == sum([int(c)**digits for c in str(n)])
for n in xrange(100,1000):
    if narcissist(n):
        print n
        break

Asma Rasheed
Mar 18, 2015

153=1^3+5^3+3^3

=1+125+27

=153

Gagan Raj
Mar 17, 2015

A narcissistic number is that number where the sums of the cubes of the digits is equal to the number itself.

The smallest 3 d i g i t 3-digit narcissistic number is 153.

How do you know that's the smallest possible?

Calvin Lin Staff - 6 years, 2 months ago

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Good query. Guess a quick few line of codes in your favorite programming language will deliver the result.

Swarup Bhattacharjee - 6 years, 2 months ago

Yes a code can prove that.....according to my knowledge i think 153 153 is the smallest one but i still dont have any rigourous proof for why is it so sir.....my methodology would still be exhaustive testing(a very old method which consumes more time and energy) but i would like to know a better proof for the same !!!!!

Gagan Raj - 6 years, 2 months ago

It is not necessarily that it is a cube only but we are talking of a three digit narcissistic number that is why it is cube of the digits. It is a number that is the sum of its own digits each raised to the power of the number of digits.

Tushar Malik - 6 years, 2 months ago

Does narcissistic number here means Armstrong number?

Siddharth Singh - 6 years, 2 months ago

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Yes it can also mean as an Armstrong number !!!!!

Gagan Raj - 6 years, 2 months ago

Yup.

Brock Brown - 6 years, 2 months ago

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