Commentary on the Einstein Maze

From Mark:

Hi Cliff. Nice maze. It took me about 3 minutes, but I typically "cheat" and do mazes backward unless it is specified that I MUST complete them forward. On average it takes me about twice as long to do a maze forward, so if you're keep statistics on this mark me down for something like 6-7 minutes.

To answer some of your questions:

1. I gave the maze to my 6-year-old (on 9/4/05) to see what she could do with it. Now, she's not a normal 6 year old, as she's able to multiply by 2 and 5 pretty easily, and has been reading at the 4th or 5th grade level since she was about 4 1/2 (my 3 year old is more "normal"). BUT, she doesn't enjoy reading books designed with 4th and 5th grade topics in mind - she finds it completely boring. Little House books or Bobsey Twins books hold no interest for her, although she can read them out loud to us with ease. Why do I include this shameless boasting? Because the same principle applies to the maze. She worked her way through about half of it in about 7 minutes, but then she lost her interest in it and put it down because she was bored. COULD a child under 7 solve the maze? Probably. But you'll have to give it to him or her in parts (in time) to keep his or her interest.

2. Not sure what makes it more difficult for some.

3. I work backward and just kind of "see" where to go. If I run into a dead end, I back up a couple spaces and try a different turn. See the bottom of this post for a spoiler involved in my method.

4. I have no idea why anyone would say it was impossible. If they exhaust all possibilities, they should find the correct path.

5 & 6. Again, I have no idea. I stay away from both, especially the illegal drugs, so I can't speak from personal experience.

7. I would use the old "always turn right" trick. It's not elegant, but it will work.

In any maze that claims to be difficult, there tends to be a portion of the maze that makes it look like you are headed steadily toward the end through the center of the maze, but it will make you double back and take a route near the outside wall. Part of "seeing" the answer is to expect such tricks. Usually twice, and sometimes three times, in any given maze.

From Twan:

Dear Cliff,
First of all I'd like to express my appreciation with your site Reality Carnival. I stumbled upon it some two months ago and check it out regularly since.

I want to react on your item Einstein Maze of 08/21/04 where you ask as question 5: "Could someone under the influence of marijuana or DMT solve this?"

I tried this by smoking joints until I could feel being under the influence (feeling high or stoned). I was able to solve the puzzle 3 times in a row, which took me the following times:

1st try: 9 min., 2nd try: 11 min., 3rd try: 8 min.

(Measured by watching my PC's clock, so these number should be taken with a grain of salt.)

What I find interesting is that my performance doesn't improve significantly on consecutive tries, the 2nd try took longer even while I just solved that same puzzle. I'd expect solving a maze puzzle to become easier on consecutive tries and that's also my experience. I also found 'backtracking' after I found a dead end surprisingly difficult. I got confused several times on each try so much that I had to start over. Maybe I experienced an impairment of short-term memory while being under the influence of THC? I guess I should repeat this little experiment when I'm sober.

Anyway, I think I can answer your question 5 positively.

Regards, Twan.

From Kyle:
Could a child under the age of 7 ever solve such a maze? yes, i think a determined child could do it rather quickly.

What makes a maze drawn in this manner more difficult to solve than a traditional "2-D" maze? uh...just that it's not quite what we're used to, and it's not what we expect to deal with when presented with a maze.

What is the best method for solving this maze? i used the mouse pointer as a guide, so i just moved around the maze with my trackball until i found the way.

Why do people claim it is impossible to solve? they didn't try hard enough.

Could someone under the influence of marijuana or DMT solve this? i am currently under the influence of maijuana and it took me about 3 or 4 minutes to solve it. i have never tried dmt, so i can't speak from experience about that. from what i've heard, probably not. at least not for the first few minutes.

How does caffeine affect the speed at which someone solves this maze? i don't know

If this maze were constructed with high walls and a grass floor, and you had to walk through it, how would you solve it? i would try to make a map of it as i went and keep track of where i was.

From Henry:
Perhaps there's something to be said for starting the maze in the middle i.e.pick some middle cells and see how far you can extnd your line in each dirction before dead ends. Dead ends will certainly eliminate certain boxes from the andswer "tree". Has anyone devise a way toeliminate certain dead end ways on a computer, yet ? I would think ten years out if one scanned in a maze to a robot "pal" and said show me the dead ends (but not the answer) quick as a wink you'd have this solved.

From Todd:
The first computer program I ever ran was a 3-D maze generator on an Apple 2 (1975?) I have a couple such 3d maze programs on various hardware which I still like better than overhead mazes. You have no backward search capability (well, some apps let you view the maze.) It's more like being in a real maze, having to find your way by backtracking (some apps let you drop breadcrumbs.) I'm running one on my Palm Tungsten T3 right now

From Davy:
1) Pass
2) For me, personally, I think the high contrast is an issue. Things like that always make my eyes bug. I also think that when we look at a maze we see "cells" and we expect the cell wall to either be there or not be there. In this puzzle you either have a solid wall, or a wall with a very narrow opening. Its easy for your eyes to gloss over the picture and mistake a wall from a door.
3) I think I spent two minutes on the "best looking guess" method. I finally went back to the tried and true "right hand rule" which finally did the job in about three more minutes. I have to admit that it still took me three tries with the right hand rule because my eyes were making me walk through walls (see above).
4) One strong possibility because it is so easy to mistake doors for walls people might think that the entrance and exit aren't really connected. On two of my failed passes I thought I was blocked in.
5) Pass
6) I did not test, but I might guess that it could SLOW them down. Again, the high contract makes my eyes jitter - cafeine might just make them jitter more causing me to get lost more frequently.
7) Again, right hand rule - it never fails.
8) I don't know if I would add a question, but I do wonder if you made a copy of the maze that used a lighter green (or a pastel blue) so that it wasn't so high contrast if people could do it faster.

From Adam:
I think it may be harder than a 2D maze because the brain wants to "translate" the isometric 3D representation of walls and doorways into a 2D map. I wonder if it would be easier or harder if the 3D representation were more accurate, with perspective, shadows and so on.

I didn't measure precisely, but it took me more than 5 minutes, and probably close to the 10 minutes you mentioned. I solved it forward and backward simultaneously (I never thought this was cheating, but afterwards I saw someone else's comments suggesting that it's easier to go backwards.)

As I worked through it, I ignored the 3D aspect and looked at it as though it were a normal maze, but with partly obscured openings. I found my internal "translation" sometimes kicking in despite my effort to suppress it. I also experienced "flipping", similarly to what happens with some 3D optical illusions that can appear either concave or convex.

I'm probably probably better than average at this. I'm a graphic designer, I can draw in perspective, view the various kinds of stereograms very easily, etc. People who are not used to visualizing things in 3D might find this very hard, leading them to decide that it's impossible.

From Tane:
hello there Cliff,

It took me ~1-2 minutes to complete (I didn't actually time myself, so I'm not *sure*), although I did it backwards - I'm quite certain it would of taken me longer had I done it forwards. Anyway, the purpose of this email is to voice my opinion on question 5 ('Could someone under the influence of marijuana or DMT solve this?'). Generally speaking, peoples perception of objects and colour is greatly enhanced when under the influence of marijuana. I have never done extensive research on the matter, but if I recall correctly, when 'stoned' - you become more of the opposite of what you usually are. As, again generally speaking, most people are at the logical/mathematical/whatever end of the spectrum, this would lead me to believe that their artistic senses kick in - hence the enhanced perception of both objects and colour. So, if the previous is true, I think that an individuals chances of solving the maze would actually be *increased* if they tried it while 'stoned'..

Then again, my whole argument is based on memories ... so the accuracy is indeed questionable.

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