The Persistence Of Memory

The Memory Labyrinth Rules

  • You are currently just behind the door in the bottom right.
  • You must walk through each of the other rooms before returning to the first room. Steps must be to horizontally or vertically adjacent tiles - no diagonal movement.
  • You may not step on the same tile twice.
  • In the middle room, you must step on every tile. In the left room, you must step on every tilein the S-shaped region.
  • Every time you step between two tiles, a line will be drawn between those two tiles' centers. This means that the line will trace out your path along the tiles, moving like a rook in chess.
  • The most important rule: When your path is completed, every section of the same color and shape must look identical. (If you enter two blue rectangles from the bottom left going up, your paths through them must be exactly the same. You can trace them out in reverse, but the lines left behind must be identical.)

Here's where I'm up to so far. Red lines indicate the path, and solid black lines are walls (i.e. I've determined it's impossible for a path to go through).

Puzzle progress

Did I misread the puzzle? One of the rules states that in the left room, "You must step on every tile in the s-shaped region". I peeked at the solution and it seems that you have to step on every tile in the room, which would help with further deductions.

It could also be just because I'm a beginner at grid deduction puzzles though.

  • $\begingroup$ @bobble Thanks for the edit. Do I really not need to hide partial solutions and information from the full solution? I felt as though that would be unfair to people who haven't tried the puzzle yet, hence the spoiler $\endgroup$ Commented Apr 23 at 1:21
  • $\begingroup$ Some immediate deductions: you can copy some walls for the dark green and cyan regions in the bottom room. Then you have to go through the light yellow tile, which seems to open up a lot of deductions in the top room. $\endgroup$
    – Bubbler
    Commented Apr 23 at 1:40
  • 1
    $\begingroup$ @ApexPolenta That's why I both added the name of the puzzle to the title and put the rules at the top. So, if someone is intrigued, they can click over to the puzzle instead of scrolling down, and they'll have no spoilers $\endgroup$
    – bobble
    Commented Apr 23 at 3:39

1 Answer 1


Here are a few deductions you could make but apparently haven't yet, all focused on that room at the left:

  • Look at the topmost pink shape. Call the tile to its right T. Because of the way T is nestled against the wall, if the path visits T it does so through two of the edges T shares with the pink shape. So in each of the other instances of that shape, there are either 0 or 2 path edges between the shape and the tile corresponding to T, which means that those tiles-corresponding-to-T can't have a path-edge out through their right side either. This e.g. lets you extend the path at the bottom right of the left room.

  • The path goes between the top right and bottom right of the left room. So it must cross any horizontal line within that room an odd number of times. In particular, where you've drawn a "wall" extending most of the way across the room you can actually extend it all the way to the right.

  • Near the top left of the lower section of the room, you can extend the path by a few squares.

At this point the lower part of the left room looks like this:

enter image description here

so now look at the horizontal line two grid-lines below the one dividing the upper and lower parts of the room. It must be crossed exactly once more by the path: either at the right or in the middle. But doing it at the right gives you a path that goes from top left to bottom right of this half-room without any way of reaching the lower-left part:

enter image description here

and that won't do. So it has to be at the right. One can make quite a lot more deductions from here, but this seems like a reasonable point to let you get on with it on your own again :-).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.