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In the heart of a mysterious labyrinth, you, the intrepid explorer, found yourself accompanied by a peculiar shadow of yourself, both adorned in distinct blue attire. This enigmatic doppelgänger mirrored your every move, whether it be left, right, up, or down. Together, you ventured forth, driven by the desire to unravel the labyrinth's secrets and escape its confounding maze.

As you navigated the labyrinth's intricate corridors, you discovered a series of glowing yellow buttons scattered throughout its passages. The purpose of these buttons remained elusive, but your intuition suggested that simultaneous activation was the key to unlocking the path to freedom.

As you delved deeper into the labyrinth's bewildering corridors, you and your shadow-self coordinated your movements flawlessly. When you went left, your shadow-self ventured right, ensuring that every step you took was mirrored. Together, you charted a course on the white tiles, carefully considering the consequences of your choices. If one of you were to encounter a wall, the other would seize the opportunity to maneuver freely, ensuring your journey continued unimpeded.

Together, you forged ahead, unraveling the labyrinth's secrets, as the bond between you and your shadow-self grew stronger with every step. Guided by your shared determination and the imminent threat of the labyrinth's impending seal, you raced against time, knowing that finding the shortest path was the key to securing your freedom before the final moments slipped away, forever trapping you within the maze's confounding depths.

puzzle

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  • $\begingroup$ It looks like the time has run out, because all exits are sealed already. More seriously, how are we supposed to figure out what the yellow buttons do? And does your shadow move down when you move up? $\endgroup$
    – Florian F
    Jul 8, 2023 at 21:39
  • $\begingroup$ So what if when I move right, my shadow can't move left because it would slam into a wall? Would it just stay there? $\endgroup$ Jul 8, 2023 at 22:01
  • $\begingroup$ Also, "finding the shortest path" => how do you measure the length of a path then? Is it the sum of the paths for me and my shadow? Or some other metric? I believe it doesn't matter which one is 'you' or which one is 'your shadow' because the only important thing is that each person moves opposite to each other when possible. $\endgroup$ Jul 8, 2023 at 23:47
  • $\begingroup$ Sorry, it is not clear what the yellow buttons do. They are supposed to be activated at the same time. Moreover, @newQOpenGLWidget if one slams into a wall, the other can move. Also try first just finding a solution, not necessarily the shortest one. $\endgroup$
    – Z1proW
    Jul 9, 2023 at 9:58
  • $\begingroup$ Thanks for the explanation. Can you edit that into the question so that future answerers more clearly know? $\endgroup$ Jul 9, 2023 at 13:12

2 Answers 2

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This was super fun to work with! I love these kinds of puzzles.

  • I found a path in 17 moves (considering every two steps in the grid is a move)

I'll use this simplified representation of the maze:

enter image description here

Note that we are donned in red attire. This is just to distinguish between the two.

We move right twice and our shadow moves left twice. In total this is 4 moves. enter image description here

Now note that both us and our shadow are against a corner, restricted in the directions they can move. This is helpful for when we want one of us to move one way but the other to make barely any move at all.

We dash up left and our shadow can just move right. This is 4 moves. enter image description here

Now, we move down while our shadow mirrors it. This is 2 moves. enter image description here

We are trapped in a corner again but can issue right 2 down 3 to our shadow. enter image description here

This is 5 moves.

Almost there! Now, we finish up with left and our shadow moves right. This is 2 moves. enter image description here

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  • $\begingroup$ You're supposed to get to the yellow squares? $\endgroup$
    – msh210
    Jul 9, 2023 at 13:24
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    $\begingroup$ @msh210 Logical assumption; how else can you 'activate' them? $\endgroup$ Jul 9, 2023 at 13:25
  • $\begingroup$ You have the blue path rotated 180 degrees relative to the red path. I interpreted the puzzle as wanting the them left-right mirrored (so they would move in the same direction up/down). $\endgroup$
    – fljx
    Jul 9, 2023 at 15:12
  • $\begingroup$ @2012rcampion Oops! I'll fix that. (P. S. that actually makes it 17 again, which is annoying. Maybe 17 is the shortest path.) $\endgroup$ Jul 9, 2023 at 15:19
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    $\begingroup$ @msh210 in the comments to the question, the OP explained more clearly: Sorry, it is not clear what the yellow buttons do. They are supposed to be activated at the same time. $\endgroup$ Jul 9, 2023 at 18:32
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A bit shorter solution, counting each square as 1 move (and only counting 1 if both you and your shadow move at the same time). (Under this metric the previous solution is 24 moves.)

The key is that...

...while in a grey square a player is completely prevented from moving in one axis, allowing the other player to move freely in two directions.

18 moves (assuming up-down motions are reflected)

21 moves (assuming only left-right motions are reflected)

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  • $\begingroup$ Good job ! You weren't supposed to move on the grey squares, but I guess it wasn't clear. I'll edit my post to include that as well. $\endgroup$
    – Z1proW
    Jul 9, 2023 at 18:22
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    $\begingroup$ Wow - this is really nice (I like how you accounted for different interpretations and used the layout of the grid to your advantage more than I did). Also I'm wondering if you could do a depth-first-search esque algorithm for this. $\endgroup$ Jul 9, 2023 at 18:35
  • $\begingroup$ @new I just used FindShortestPath, I think it uses Dijkstra's algorithm internally for unweighted graphs. $\endgroup$ Jul 9, 2023 at 21:20

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