Other than barging through the corn like a crazy person, is the simple solution to a maze to just follow the right or left wall all the way out if you get lost? Does it work the same way to go through the maze, start to finish?
Is it possible to design a static maze that doesn’t follow that rule, if true? Is the follow-the-right-wall rule the optimal solution, the longest solution, or does it depend?
Please answer, am getting cold.
Assuming that the exit is on the same wall (it can be on any side - if the maze is a rectangle) as the entrance, following the right (or left) wall always leads to the exit, although it may be a very non-optimal solution. If the exit is in the “inside” of the maze (say, an door to a tunnel), then this solution may not work.
You can build a maze where that doesn’t work. Here’s a short article on NYTimes about the family that called 911 when they were lost in a maze. They have some relevant quotes from a corn maze designer.
Of course, this approach is only guaranteed to work if you follow it from the beginning. If you realize you’re lost and then start, you could just go in circles.
You can also make it so that doesn’t work by making the maze three-dimensional, or by making it change with time (though that would be difficult in a corn maze, unless you have some very fast-growing corn).
I’m perplexed by the family lost in the corn maze. Corn is planted in rows. Surely they could have simply walked out of the maze by following the corn row, right?
Relevant points to add:
This is true (for a two dimensional maze) only if there are points inside the outermost borders of the maze which cannot be reached by any path from the entrance.
AND
If it does happen, then once one has discovered it’s happening (for example via a mark on the wall) one can simply switch to the opposite wall. A cleverly designed maze, though, could make it confusing to figure out what wall segments belong to which wall… ETA: But not if you’re allowed to make a continuous line on the wall.
Only if you define “unreachable points” as including points on the walls themselves. You could put a “tree” of walls, without any loops, somewhere in the interior of the maze, and a would-be solver might end up just tracing around the outside of that tree.
Example very simple maze:
+---+
| Exit
|A| |
| | |
| Entrance
+---+
If you’re at point A, facing north, when you decide you’re lost, and follow the right wall, you’ll never get out.
I did mean it to include points on the walls themselves, but I hadn’t thought through how trivial this makes the claim. What I had in mind was the possibility of loops and single points (i.e. idealized column-like “walls”), but I failed to notice that a line all by itself (as in your graph) also constitutes a set of unreachable points.
Some corn mazes include bridges which could easily defeat this plan.
It doesn’t matter in any way shape or form if the maze is 2d/3d, has tunnels, bridges or exits on a different wall or anything. If you follow a single wall from start to finish you will get out. (You may end up leaving the same entry you came in or a different one.)
There are two possibilities in following a fixed strategy in a maze: either you get out or you end up looping inside. Following a wall will never loop. There is no point where the wall you are following can close in on itself and form a loop.
(It is known that you can fully traverse any 2d maze using a simple strategy and two markers that you can drop and pick up. It’s very slow though. Manuel Blum, Dexter Kozen. “On the Power of the Compass (or, Why Mazes Are Easier to Search than Graphs)” FOCS, 1978, pp132-142.)
For a 3-D maze, the definition of “follow a single wall” may become ambiguous. Consider another simple maze, consisting of a single dead-end corridor with an oubliette pit at the end of it. You go down the corridor, fall in a pit, and continue to trace out the wall of the oubliette forever.
Or, if you object that falling into the pit doesn’t count as “following the wall”, make it a spiral staircase that goes down into the pit. Now, if you keep following the wall, you’ll eventually end up with the wall being the side of the staircase, which dwindles down to nothingness at the floor.
Good point. I didn’t really mean 3d in the full sense. Just stuff that humans can walk thru in a standard way. A simple floor, 2 walls on either side with simple side only branches. I was thinking of bridges and tunnels type 3d-ness. No ambiguity about “the wall” allowed.
In your example, “the wall” branches. One part continues on past the pit and the other goes down.
That’s correct. The corn maze near me has a bridge at the exit, so the “end” is actually towards the center of the maze, and then you go across the bridge to get out of the corn.
Slightly off topic question; just how tough are corn plants? My immediate thought when I read that news item about a family calling 911 was why didn’t the adults just force their way through the corn in a more or less straight line?
Not necessarily. It is possible that you are sandwiched between 2 different interior circles, in which case you would have to continue until you reach a point connected to an exterior wall.
Regarding the bridges, I was imagining a bridge/tunnel that starts and ends in the middle of a room, and so not connected to any wall. A solution then is to artificially imagine that the bridge/tunnel is connected to one of the walls both before at the start and at the end, and then continue to trace your way.
I am curious about this. In order to defeat the follow the wall rule, the wall has to “split” somehow. Is there a place where there is a stairs and you can opt to go straight or up the stairs, e.g., with the same wall continuing in both directions?
But a slight variant still allows a simple traverse of the maze, assuming the number of such splits is small enough to remember each one and which choice you made each time.
Corn is very easy to push aside and walk through but some cornfields can be huge and you might have to walk for a very long time in a straight line before you hit a fence or road. Even when you get out of the field you may not know where you are, not all country roads are well marked.
In a corn maze, they don’t plant the corn that way. You can push your way out, of course, but only by doing some damage to the maze itself, which is a bit uncool. Not, mind you, that it’s *more *cool to dial 911. But I can sympathize a little with the people who got lost. It’s surprisingly easy to do, especially if you let a seven-year-old choose which direction to go. That’s the voice of experience speaking, by the way.
Well, I have a plan for defeating that.
Poison Ivy mazes.