So, I'm playing a game (The Da Vinci Code) and are really stuck on a 2x3 tile sliding puzzle. It looks something like this

1 - 5 - 4

2 - x - 3

and it has to look like this:

1 - 4 - 5

2 - 3 - x

if anyone has any idea how to solve it I would appreciate it.


1 Answer 1


This is impossible.

With the 15 Puzzle and its variants, you can only ever reach half of the possible configurations. In particular, if you can reach a configuration, you cannot ever reach a single swap away from that configuration (but you can always reach any two swaps away, and you cannot reach three...)

Here, you can reach one swap away from your goal by just pushing the 3 left. So you cannot reach the goal itself.

  • $\begingroup$ How is swap defined here? Just a swap between two tiles? I guess there must be a lateral solution to the OPs puzzle. Like turning the puzzle upside-down? $\endgroup$
    – Dr Xorile
    Sep 17, 2019 at 3:47
  • $\begingroup$ @DrXorile Yes, just a swap between two tiles. And even that won't work - when there's a hole in the center, turning the puzzle upside down is just two swaps of opposite corners plus a single move, so parity is maintained. (And when the hole is somewhere else, that's just a move, a flip as above, and a move back, all of which maintain parity.) $\endgroup$
    – Deusovi
    Sep 17, 2019 at 3:50
  • $\begingroup$ Could it be that the video game is poorly made then? $\endgroup$
    – BurnedP
    Sep 17, 2019 at 19:40
  • $\begingroup$ @BurnedP Yes, that would be my best guess. Either that or there's some sort of trick to it. $\endgroup$
    – Deusovi
    Sep 18, 2019 at 1:47

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