Why is my rubik's cube calculation off by 4000?

Question

I'm trying to throw together some quick and dirty javascript code to give me the number of possible piece permutations on a rubik's cube given a constraint such as "1 edgepiece is solved". (sticking to 3x3 for simplicity) When I run the normal 12 edgepieces and 8 corners through my function, it's giving me a number that is 4000 greater than what I'm able to find should be the answer. (Function gives me 43,252,003,274,489,860,000 but https://www.youtube.com/watch?v=z2-d0x_qxSM says it should be 43,252,003,274,489,856,000)

My code:

// 3x3x3 Rubik's Cube
edgepieces = 12;
cornerpieces = 8;
centerpieces = 6;

// total possible permutations in general
function numCombos(edges, corners) {
    result = ((factorial(edges) * (factorial(corners)) / 2) * (2 ** (edges - 1)) * (3 ** (corners - 1)));
    return result;
}

// n!
function factorial(x) {
    if (x == 0) {
        return 1;
    } else {
        return x * factorial(x - 1);
    }   
}

console.log(numCombos(edgepieces, cornerpieces) + '\n');

I have followed a couple different arrangements for the core result algorithm, and they all give me this end result. What am I missing?

Answer 1

You can use BigInt values to avoid floating-point precision issues:

// 3x3x3 Rubik's Cube
edgepieces = 12n;
cornerpieces = 8n;
centerpieces = 6n;

// total possible permutations in general
function numCombos(edges, corners) {
    result = ((factorial(edges) * (factorial(corners)) / 2n) * (2n ** (edges - 1n)) * (3n ** (corners - 1n)));
    return result;
}

// n!
function factorial(x) {
    if (x == 0) {
        return 1n;
    } else {
        return x * factorial(x - 1n);
    }   
}

console.log(numCombos(edgepieces, cornerpieces) + '\n');