Digit factorials: Find the Sum of All the Curious Numbers

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
Find the sum of all numbers which are equal to the sum of the factorial of their digits.
Note: as 1! = 1 and 2! = 2 are not sums they are not included.

Pre-computing the Digit factorials

The factorials we all need to know are from 0! to 9!. Therefore, we can pre-compute the digital factorials and store them in a dictionary (or hash map).

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let factorials = {};
let s = 1;
for (let i = 1; i <= 9; ++ i) {
    s *= i;
    factorials[i] = s;
}
factorials[0] = 1;

let factorials = {};
let s = 1;
for (let i = 1; i <= 9; ++ i) {
    s *= i;
    factorials[i] = s;
}
factorials[0] = 1;

A single loop from 1 to 9 is sufficient as we are iteratively multiple the next number.

Uppper bound of the Curious Numbers

We don’t need to and we can’t search infinite numbers. One upperbound we can use is 9999999 as 7*9! is less than 9999999.

We then bruteforce all the numbers and sum those curious numbers. The curious number can be determined by the following procedure: converted to string, and split into char array, then sum up the digital factorials, finally comparing the sum with the number.

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let sum = 0;
for (let i = 3; i <= 9999999; ++ i) {
    let x = String(i).split('').reduce((a, b) => {
        return a + factorials[b];
    }, 0);
    if (x === i) {
        sum += i;
    }
}
console.log(sum);

let sum = 0;
for (let i = 3; i <= 9999999; ++ i) {
    let x = String(i).split('').reduce((a, b) => {
        return a + factorials[b];
    }, 0);
    if (x === i) {
        sum += i;
    }
}
console.log(sum);

The answer is 40730.

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