created by Bobula_Rossa on 02/12/2024 at 17:26 UTC
238 upvotes, 22 top-level comments (showing 22)
A two-dimensional maze is laid on the floor. This maze is like one you might find in a kids coloring book. It has an entrance and exit, and a single path can be drawn to the exit. Instead of paths, this maze is composed of water pipes.
Suppose the maze is entirely filled with water and the entrance is attached to a pressurized water hose. In a small maze, the water would flow to and out the exit and complete the path. The water pressure "solved" the maze.
Is there a size of maze where the water pressure is not enough to solve? Can the maze be infinitely spread across the floor? Can it scale up as long as there is enough water pressure? Is there a point where no amount of water pressure would be enough?
Comment by MyMomSaysIAmCool at 02/12/2024 at 19:35 UTC
414 upvotes, 6 direct replies
Water will solve any maze, two or three dimensional. However, it won't just find one exit or all exits. It'll find just enough exits to let it leave the maze at the same rate that it enters the maze.
You could make a 3d maze that has "wrong exits". If those wrong exits are below the level of the correct exit, then the water would not solve the maze.
But then you could increase the flow until the water overwhelmed the wrong exits. At that point, the water level would rise, and water would begin coming out of the correct exit.
Comment by ramriot at 02/12/2024 at 19:49 UTC
13 upvotes, 1 direct replies
There are a bunch of simplifications one would make to model such that cannot be left out to solve many if the questions asked.
For example surface effects, corner effects & turbulence are usually neglected or assumed to have a simple relationship.
For example, say the shortest path has many turns while a longer path has many fewer. A simple model would suggest water will opt for the shortest path showing the greatest flow, but all those turns would slow the flow & make a longer path the solution.
Interestingly, in other modelling cases, when I compare my route to work as suggested by Google & by my in car GPS ignoring traffic as there is none, Google's chosen route is longer by 2Km but uses less fuel & takes about the same time as the shorter zigzag path my car chooses.
Comment by Mueller96 at 03/12/2024 at 09:39 UTC
9 upvotes, 1 direct replies
You should check out the video made by Steve mould on this topic. It doesn’t fully answer all your questions, but it should give you a better understanding of the basics for your scenario. Overall I would say it will solve any maze as long as the pressure is enough to overcome the friction
Comment by Deto at 02/12/2024 at 22:04 UTC
15 upvotes, 0 direct replies
The water doesn't automatically 'know' where to go when it hits an intersection. What happens is that initially the pressure will spread out down every path. However once it hits the dead ends of other paths you get these transient reflections back that ultimately cause the pressure at the 'wrong direction' path to be equal to the pressure at the input of the intersection (and therefore, water flow m down that path ceases). For the correct input, you'll still get transient effects but when these settle down the pressure will be slightly lower allowing for steady state flow.
So, for an infinitely long maze the water down each path will never hit an 'end' and pressure will never have to equalize. It'll just flow down all paths forever. Or maybe the answer is that 'yea' water can solve an infinitely large maze but it will need an infinite amount of time to reach equilibrium steady state pressure/flow (so the maze is never really solved actually).
Comment by Mavian23 at 02/12/2024 at 19:30 UTC
25 upvotes, 5 direct replies
Wait, if the maze is entirely filled with water from the start, how do you trace the path that the new water takes through the maze? Wouldn't the maze just always be filled with water, even while the pressurized hose is turned on? Do you maybe have a colored water come out of the pressurized hose?
Comment by abnormalbrain at 03/12/2024 at 03:12 UTC
5 upvotes, 0 direct replies
Ok lemme try something.
The answer is no. It will not "solve" the maze. It can fill the maze, but as for being a tool or agent that can be used to determine the maze's one, true solution, and dismissing false routes, no.
It would basically be like using air to solve it. Even if you pressurize it, the best you'd achieve is learning the input and output. Release confetti in the liquid or gas to trace the route and each piece would only demonstrate randomness.
Comment by Improbabilities at 02/12/2024 at 20:32 UTC
3 upvotes, 1 direct replies
The water has to go somewhere. The only reason it wouldn’t come out the exit is if the surface tension / friction of the water against the walls is stronger than the water pressure going in, which doesn’t really seem possible
Comment by Blackbear0101 at 02/12/2024 at 21:05 UTC
6 upvotes, 0 direct replies
This is a « spherical cow in a vacuum » kind of problem.
Theoretically, if you have a maze with one way in and one way out, regardless of where the way in and the way out are in the maze, water will solve the maze, as long as you have an infinite supply of water and an infinitely powerful pump.
In reality, it’s not that simple. First, water would loose energy by flowing in that maze, and infinitely powerful pumps do not exist. You can solve that problem by having the water flow very slowly, because slower flow means almost no energy loss.
You also have the problem of how much water you have. For example, you can have a very simple « maze that’s just a 1000 cubic meter cube, with the water in at the bottom and the way out at the top. If you have less than 1000 cubic meters of water, it’s never going to solve that maze, even though you can see the exit.
The third problem is leaks. Let’s say you actually build a maze using pipe. If there are enough leaks in that pipe maze to make it so the total flow in leaks out before even getting to the true exit, you’re never solving that maze using water either.
Comment by ledow at 02/12/2024 at 21:06 UTC
2 upvotes, 0 direct replies
Yep. And "simulating" that is precisely how many maze-solving /path-finding algorithms work.
Maths takes from physics sometimes. You know the way to find the longest route on a "graph" (think of a graph as a series of towns connected with roads)? Make the roads be ropes. Tie them together where they meet in a town. Now pick up any knot (town). Then let the rest drop under gravity. Now pick up the lowest knot. Between those two knots that you picked up is the longest single journey (without loops etc.).
It's used in routing algorithms to find, e.g. the worst case scenario for fuel or the longest latency on a set of cellilar masts.
Comment by scraperbase at 04/12/2024 at 09:16 UTC
2 upvotes, 1 direct replies
How would water solve the maze? It would just flow everywhere and at one point it will come out of an exit, but you already know where the exit is anyway. That will not give you any additional information. You might think you could just use a ball and let the water pressure put it through the maze until it finally reaches the exit. That will not work though. The ball will reach a dead end at some point and stay there. It will not flow backwards.
Comment by felidaekamiguru at 02/12/2024 at 19:50 UTC
3 upvotes, 1 direct replies
Is there a size of maze where the water pressure is not enough to solve?
Very Big^TM
Can the maze be infinitely spread across the floor?
That definitely qualifies as Very Big^TM
Can it scale up as long as there is enough water pressure?
Within any finite maze, yes
Is there a point where no amount of water pressure would be enough?
That infinite maze would absorb any finite amount of water, so if the exit were infinitely far away, it would keep absorbing water forever. Once forever ended, you might get water out the exit.
Infinity is a funny thing. It often breaks everything.
Comment by cjgeist at 02/12/2024 at 19:39 UTC
1 upvotes, 1 direct replies
I think it's not so much about the pressure of the water as the quantity. Lying flat on the ground, the water will spread out in all directions it can, until either it reaches the exit, or the layer is too thin to keep sliding across the surface. If you keep adding water it will eventually drain out the exit
Comment by [deleted] at 02/12/2024 at 20:13 UTC
1 upvotes, 1 direct replies
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Comment by [deleted] at 02/12/2024 at 20:27 UTC
1 upvotes, 1 direct replies
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Comment by bajsplockare at 02/12/2024 at 23:00 UTC
1 upvotes, 0 direct replies
You can use Bernolli's equation with a loss factor dependent on the material of the walls to calculate the pressure needed to get the water flowing, since a bigger maze will increase friction, it will require higher pressure. However if you increase the pressure too much the outer walls might break.
Comment by mackstrife at 02/12/2024 at 23:10 UTC
1 upvotes, 0 direct replies
When we are talking infinity. The longer the maze the more pressure needed to push the water.
Unless the stress resistance of the pipe is also infinite eventually the amount of pressure needed to push the water would cause the pipe to explode.
This is theoretical of course since the amount of pipe needed would be ridiculous.
Comment by Tim_the_geek at 02/12/2024 at 23:40 UTC
1 upvotes, 0 direct replies
If you made the maze slightly raised, with the exit slightly lower. Next add water, the water will fill the entire maze, until it poursover the exit threshold. Now you can float an object on the water, it will go directly to the exit.
Comment by ReflxFighter at 04/12/2024 at 06:34 UTC
1 upvotes, 0 direct replies
This gives similar vibes to the maze solving robot that has to extinguish a candle, which it did by not traveling and smashing a piece of dry ice to make the co2 it sublimates snuff out the candle from anywhere in the maze
Comment by theOnlyDaive at 04/12/2024 at 21:31 UTC
1 upvotes, 0 direct replies
Paths that do not lead to an exit will fill and pressurize. The exit will allow flow, so water will go there (path of least resistance and all). Depending on the structure, the rest of the maze may have to fill before the water reaches the exit. Nature likes to spread out and be all balanced and such.
Comment by VoidCoelacanth at 06/12/2024 at 03:51 UTC
1 upvotes, 1 direct replies
Consider this:
Water exiting the maze does not mean the maze is *solved.*
To *solve* a puzzle or problem implies that you know the mechanisms that achieve the answer.
If you put pressurized water into one end of a pipe maze, and open the exit, water will flow out - but it has not revealed to you, the observer, *the path it used to get from entrance to exit.*
Therefore, all you have truly learned is that *an unobstructed path from Entrance to Exit does in fact exist,* but you do not know what that path is.
Given all of this - I would say no, water (nor any other fluid) cannot "solve" a maze on its own. You would need to be able to see the flow of the water, meaning clear pipes and a dye agent or other means of detecting the path of flow.
Comment by 314159265358979326 at 02/12/2024 at 19:42 UTC
1 upvotes, 0 direct replies
When it's infinitely spread out, you have infinite friction loss and gravity won't be able to overcome it in a finite amount of time.
I don't know the maze problem but I do know water pressure, and in a scenario with gravity for a finite, 2D maze it ought to work.
Comment by pemcil at 03/12/2024 at 01:45 UTC
-3 upvotes, 0 direct replies
Yes. When you attempt to solve the maze with a pen, the ink is 2D liquid. If you take a wrong course you have filled it with liquid. Fill all the wrong courses with liquid if you must, but the liquid will still reach the exit.