Search code examples
mathmatrixpuzzlecomputation

Puzzle - 2*4 Matrix

I am trying to figure out if there is a solution to the below matrix. Source Matrix:

| 1 2 |
| 3 4 |
| 5 6 |
| 7 X |

'X' is a vacant position, and you can move you numbers around 'X'.

Can you arrange the numbers in such a way that it becomes a continuous sequence:

| 1 2 |
| 4 3 |
| 5 6 |
| X 7 |

If yes, then how??

Solution

  • It is not possible. The parity of "X-less snake permutation" preserves for every move. Source matrix corresponds to snake permutation 124356x7 = 1243567 - odd. Destination matrix corresponds to snake permutation 1234567x = 1234567 - even.