---
id: 6a22d77ddf034bc4e35b1d5d
title: "Challenge 356: Magic Square Solver"
challengeType: 28
dashedName: challenge-356
---

# --description--

Given a 3x3 grid with one missing number (represented as `0`), return the missing number that completes the magic square, or `"impossible"` if no valid number exists.

A magic square is a grid where every row, column, and diagonal adds up to the same number.

# --hints--

`solveMagicSquare([[2, 7, 6], [9, 0, 1], [4, 3, 8]])` should return `5`.

```js
assert.equal(solveMagicSquare([[2, 7, 6], [9, 0, 1], [4, 3, 8]]), 5);
```

`solveMagicSquare([[0, 14, 12], [18, 10, 2], [8, 6, 16]])` should return `4`.

```js
assert.equal(solveMagicSquare([[0, 14, 12], [18, 10, 2], [8, 6, 16]]), 4);
```

`solveMagicSquare([[12, 17, 16], [19, 0, 10], [14, 13, 18]])` should return `"impossible"`.

```js
assert.equal(solveMagicSquare([[12, 17, 16], [19, 0, 10], [14, 13, 18]]), "impossible");
```

`solveMagicSquare([[15, 35, 31], [43, 27, 11], [23, 19, 0]])` should return `39`.

```js
assert.equal(solveMagicSquare([[15, 35, 31], [43, 27, 11], [23, 19, 0]]), 39);
```

`solveMagicSquare([[26, 41, 14], [47, 35, 0], [32, 29, 44]])` should return `"impossible"`.

```js
assert.equal(solveMagicSquare([[26, 41, 14], [47, 35, 0], [32, 29, 44]]), "impossible");
```

# --seed--

## --seed-contents--

```js
function solveMagicSquare(grid) {

  return grid;
}
```

# --solutions--

```js
function solveMagicSquare(grid) {
  const flat = grid.flat();
  const zeroIndex = flat.indexOf(0);
  const row = Math.floor(zeroIndex / 3);
  const col = zeroIndex % 3;

  const target = grid.find(r => !r.includes(0))
    .reduce((sum, n) => sum + n, 0);

  const missing = target - grid[row].reduce((sum, n) => sum + n, 0);
  const filled = grid.map((r, ri) =>
    r.map((n, ci) => (ri === row && ci === col) ? missing : n)
  );

  const check = (arr) => arr.reduce((sum, n) => sum + n, 0) === target;

  for (let i = 0; i < 3; i++) {
    if (!check(filled[i])) return "impossible";
    if (!check(filled.map(r => r[i]))) return "impossible";
  }
  if (!check([filled[0][0], filled[1][1], filled[2][2]])) return "impossible";
  if (!check([filled[0][2], filled[1][1], filled[2][0]])) return "impossible";

  return missing;
}
```