Narcissistic Number

Logic Level 3

A narcissistic number is an n n -digit number that is the sum of the n th n^\text{th} powers of its digits.

For example, 153 is a narcissistic number because 153 = 1 3 + 5 3 + 3 3 153 = 1^3+5^3+3^3 .

Given that 186709961001538790100634132976990 is a narcissistic number, find the smallest narcissistic number larger than it.


The answer is 186709961001538790100634132976991.

Christopher Boo by Christopher Boo , 24, Singapore

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2 solutions

Cantdo Math
May 1, 2020

Simply observe 1 2 = 1 1^2=1 just as 0 2 = 0 0^2=0 .Hence,changing the last digit to 1 1 is enough.

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Hasmik Garyaka
Feb 1, 2019

If n is narcissistic and ends with 0, n+1 is also a narcissistic.

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