Problem 2491. Dudeney Numbers: Numbers which are the cube of their decimal sum

Created by Peter Cook

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From Wikipedia: A Dudeney number is a positive integer that is a perfect cube such that the sum of its decimal digits is equal to the cube root of the number.

For example:

512=(5+1+2)^3

4913=(4+9+1+3)^3

19683=(1+9+6+8+3)^3

Write a function that returns true if a number is a Dudeney number and false otherwise.

Assume all numbers are of base 10.

If a number is negative, assume that only the leading digit carries the negative sign e.g. -4913 -> (-4+9+1+3)^3

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Last Solution submitted on May 02, 2025

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Alex Drikitis on 14 Sep 2021

is there any negative dudeney number?

Dyuman Joshi on 14 Sep 2021

Depends upon how you define them.

If you are taking - sign outside the cube of the sum, every negative number corresponding to the positive Dudeney number is a Dudeney number.

If you define by the way OP has defined, -1 qualifies as a Dudeney number.

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Problem 2491. Dudeney Numbers: Numbers which are the cube of their decimal sum

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Problem 2491. Dudeney Numbers: Numbers which are the cube of their decimal sum

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