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Solving Greco-Latin squares for Magic Squares
// 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
);
}
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