magic-square-forming.js

function formingMagicSquare(s) {
  
  function magicSquaresOfOrder3() {
    function f(a, b) {
      // Édouard Lucas general formula for order 3 magic squares
      let c = 5
      return [
        [c - b, c + (a + b), c - a],
        [c - (a - b), c, c + (a - b)],
        [c + a, c - (a + b), c + b]
      ]
    }

    return [
      f(-1, -3),
      f(-3, -1),
      f(-1, 3),
      f(-3, 1),
      f(1, 3),
      f(3, 1),
      f(3, -1),
      f(1, -3)
    ]
  }

  let m = magicSquaresOfOrder3()
  let min = 45

  for (let i = m.length; i-- > 0;) {
    let c = 0
    for (let j = 3; j-- > 0;) {
      for (let k = 3; k-- > 0;) {
        c += Math.abs(s[j][k] - m[i][j][k])
      }
    }

    if (min > c) {
      min = c
    }
  }

  return min
}

console.log(formingMagicSquare([[5,3,4],[1,5,8],[6,4,2]]))
console.log(formingMagicSquare([[4,9,2],[3,5,7],[8,1,5]]))
console.log(formingMagicSquare([[4,8,2],[4,5,7],[6,1,6]]))