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102 lines
2.5 KiB
Markdown
102 lines
2.5 KiB
Markdown
---
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id: 6a22d77ddf034bc4e35b1d5d
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title: "Challenge 356: Magic Square Solver"
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challengeType: 29
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dashedName: challenge-356
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---
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# --description--
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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.
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A magic square is a grid where every row, column, and diagonal adds up to the same number.
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# --hints--
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`solve_magic_square([[2, 7, 6], [9, 0, 1], [4, 3, 8]])` should return `5`.
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```js
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({test: () => { runPython(`
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from unittest import TestCase
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TestCase().assertEqual(solve_magic_square([[2, 7, 6], [9, 0, 1], [4, 3, 8]]), 5)`)
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}})
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```
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`solve_magic_square([[0, 14, 12], [18, 10, 2], [8, 6, 16]])` should return `4`.
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```js
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({test: () => { runPython(`
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from unittest import TestCase
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TestCase().assertEqual(solve_magic_square([[0, 14, 12], [18, 10, 2], [8, 6, 16]]), 4)`)
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}})
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```
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`solve_magic_square([[12, 17, 16], [19, 0, 10], [14, 13, 18]])` should return `"impossible"`.
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```js
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({test: () => { runPython(`
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from unittest import TestCase
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TestCase().assertEqual(solve_magic_square([[12, 17, 16], [19, 0, 10], [14, 13, 18]]), "impossible")`)
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}})
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```
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`solve_magic_square([[15, 35, 31], [43, 27, 11], [23, 19, 0]])` should return `39`.
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```js
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({test: () => { runPython(`
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from unittest import TestCase
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TestCase().assertEqual(solve_magic_square([[15, 35, 31], [43, 27, 11], [23, 19, 0]]), 39)`)
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}})
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```
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`solve_magic_square([[26, 41, 14], [47, 35, 0], [32, 29, 44]])` should return `"impossible"`.
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```js
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({test: () => { runPython(`
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from unittest import TestCase
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TestCase().assertEqual(solve_magic_square([[26, 41, 14], [47, 35, 0], [32, 29, 44]]), "impossible")`)
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}})
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```
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# --seed--
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## --seed-contents--
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```py
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def solve_magic_square(grid):
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return grid
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```
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# --solutions--
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```py
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def solve_magic_square(grid):
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flat = [n for row in grid for n in row]
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zero_index = flat.index(0)
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row = zero_index // 3
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col = zero_index % 3
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target = next(sum(r) for r in grid if 0 not in r)
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missing = target - sum(grid[row])
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filled = [r[:] for r in grid]
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filled[row][col] = missing
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def check(arr):
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return sum(arr) == target
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for i in range(3):
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if not check(filled[i]):
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return "impossible"
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if not check([filled[r][i] for r in range(3)]):
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return "impossible"
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if not check([filled[0][0], filled[1][1], filled[2][2]]):
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return "impossible"
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if not check([filled[0][2], filled[1][1], filled[2][0]]):
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return "impossible"
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return missing
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```
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