Breaking Down the Problem

One of the aspects I appreciate about such problems is their mathematical clarity. Starting from the definition, as noted in various sources:

In number theory, a Narcissistic number (also known as a pluperfect digital invariant (PPDI) or Armstrong number) in a specific base b is a number that equals the sum of its digits raised to the power of the number of digits.

Thus, the steps to solve this problem are as follows:

1. Separate the number into its constituent digits.
2. Determine the total number of digits.
3. Raise each digit to the appropriate power.
4. Sum the results.

Finally, a simple comparison between the calculated sum and the original number will reveal whether the number is Narcissistic.

Implementing the Solution in JavaScript

Here's how I translated the aforementioned steps into JavaScript code:

export const narcissistic = (n: number): boolean =>

[...`${n}`].map(Number).reduce((a, x) => a + x ** ${n}.length, 0) === n;

Revisiting the steps:

• To extract digits:

const digits: number[] = [...`${n}`].map(Number);

• To count the digits:

const exponent: number = ${n}.length;

• To calculate the power:

const power: number = x ** exponent;

• To sum the powers:

const sum: number = digits.reduce((a, x) => a + x ** exponent, 0);

This allows us to streamline the operations into a single cohesive function. Alternatively, for better readability, the following extended version can be used:

export function narcissistic(n: number): boolean {

const digits: number[] = [...`${n}`].map(Number);

const exponent: number = digits.length;

const pow = (x: number) => x ** exponent;

const sum: number = digits.reduce((a, x) => a + pow(x), 0);

return sum === n;

}

The AI's Take on the Problem

I consulted ChatGPT, a leading AI tool, for its solution to this issue:

function isNarcissistic(num: number): boolean {

const numStr = num.toString();

const numDigits = numStr.length;

let sum = 0;

for (const digit of numStr) {

sum += Math.pow(parseInt(digit, 10), numDigits);

}

return sum === num;

}

While this solution is functional, it may lack elegance compared to others I've encountered. However, it successfully provided a correct response on the first attempt, which is commendable.

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Chapter 1: The Basics of Narcissistic Numbers

In this chapter, we'll cover the foundational concepts and definitions associated with Narcissistic Numbers, including their significance in number theory.

Section 1.1: Practical Examples