Solving Greco-Latin squares for Magic Squares

GrecoLatin2MagicSquares.js

// Replace these variables with your own
const chemEcoSquare = `A5 B4 C3 D2 E1 
E4 A3 B2 C1 D5 
D3 E2 A1 B5 C4 
C2 D1 E5 A4 B3 
B1 C5 D4 E3 A2 `;

let map = {
    A: 0,
    B: 1,
    C: 2,
    D: 3,
    E: 4,
    1: 0,
    2: 1,
    3: 2,
    4: 3,
    5: 4
};

/**
 * You can use this site to generate a Greco-latin square
 * @see https://www.chemical-ecology.net/java/r93-fig6.htm
 */
function mkSquareFromChemEco(chemEcoSquare) {
    return chemEcoSquare.split(" ")
        .map(it => it.trim())
        .filter(it => it !== "");
}

const square = mkSquareFromChemEco(chemEcoSquare);

function getBase10(square) {
    return square
        .map(it => it.split("").map(character => map[character]).join(""))
        .map(it => parseInt(it, Math.sqrt(square.length)) + 1);
}

function verify() {
    const out = getBase10(square);
    const width = Math.sqrt(out.length);

    // Make the base10 a 2d array
    const out2d = new Array(width).fill(0).map((_, i) => {
        return out.slice(i * width, (i + 1) * width);
    });
    
    const diagonal = [];
    
    for (let i = 0; i < 5; i++) {
        diagonal.push(out2d[i][i]);
    }
    
    const sum = (a, b) => a + b;
    const r1o = out2d[0].reduce(sum);
    const rws = out2d.every(it => it.reduce(sum) === r1o);
    const dgo = diagonal.reduce(sum);
    const dgs = dgo === r1o;
    
    console.debug(r1o, rws, dgo, dgs);
    
    return (
        rws && dgs
    );
}