From Unintuitive to Eureka pt.5

Behold the simple, clean, yet challenging puzzle game 3D Logic. If you haven't played it, great! This is the perfect opportunity to observe your learning process. Perhaps by comparing your thoughts to mine, we can uncover intuition gaps, where they are, and how we formed them. Play the game first, and when you get stuck, read through my process. Is there something you overlooked? A technique you didn't develop? A way of reading the cube that's more efficient?

The following is a log of my thoughts, techniques, and strategies as I developed them level by level. Keep in mind how the progression of challenges (development/pacing) is a key part of this experiment. The smoother the difficulty curve, the better the experiment.

 

This is the code I use to refer to colored nodes.

Surprisingly and unfortunately the colors in this puzzle game are not fixed. If you play the same level twice, the colors will be in different positions. While the puzzle challenge remains intact, notating solutions via colors becomes impossible. So, I used a simple code. Each face has a name (top, left, right) and I'll refer to nodes by number. Number the nodes in order reading each face from top-to-bottom and left-to-right. The white arrows in the image above indicate which direction is down for each face. So top-1 refers to the green node at the tippy top of the cube in the image above. 

Here we go! 

• 1: A very straightforward challenge on a 3x3 cube. The nodes on the left face are the simplest, while the other two colors wrap around the side of the cube. 
• 2: The left-2 line clearly is designed to help the player visualize how connections can be made across the edges of the cube. There are also 4 colors to connect instead of 3. 
• 3: Again, there's no extraneous space when you solve this level. Perhaps all levels will be like this. The top-1&2 line wraps around the entire cube. 
• 4: Top-1 wraps around the cube. Otherwise, a very straight forward challenge. 
• 5. Still solving the challenges with a simple straight-forward/linear approach. You either have to be conservative drawing the lines for top-1&2. Or you have to drawn the line for top-1 so that it doesn't cut any other line off. 
• 6: The only option is to go left from the right-1 node making a full (indirect) loop around the potential path of left-1. I will call this technique looping. 
• 7: Like level 6, this level pushes the looping concept even farther. Notice how much out of the way right-1 has to wind to not block the path of left-1. 
• 8: Now we have 3 colors. I developed a new technique where I fill in the squares from the starting state that must be filled due to space limitations; filling. Filling right-3 allows us to fill more of left-1 and right-2. After filling, the solution is linear (ie. no branches to consider). 
• 9: 5 colors! The more colors, the more space is limited. Notice how left-3 has two basic paths it can take (straight across the top face or looping onto the right face). If straight, we will completely cut off top-1,3,&4. Recognizing when one line will cut off one or more lines is call block checking. Using this technique will help narrow down options to limit any trial and error necessary. Often block checking is followed by filling. 
• 10: Filling left-3 and right-1&2. Block check and fill left-4. Loop left-3. Linear solution.
• 11: Filling left-2 and right-1,2,&3. By gradually filling the squares that must be filled, looping  right-2 becomes obvious. Linear solution.
• 12: Block checking left-1 forces the line to loop to the right. This forces top-1&3 to connect down to the right face nodes. There's lots of space to consider. The challenge can be completed with unused squares.
• 13: New technique. Flagging is when you fill out multiple possible lines to connect a single color so that when other lines cut into its territory, the remaining option(s) is left over. It's a way of marking possible routes when it's not obvious which is best. Flag every node starting with the right face and the solution becomes clear. Again there are unused squares. 
• 14: Because right-4 will block left-1 if we attempt to loop the line left, we can slowly fill in right-2,3,&4. All the lines but left-1 should be connected. The rest is linear. 
• 15: Now we're working with a 5x5x5 cube. Starting this one may seem like a stab in the dark. Recall, using our techniques we can read fail states to get a better idea of how to solve the puzzle. Tip: start with a limited color. I tend to start working with the nodes on the very perimeter. I traced two lines for left-3; 1 moving right along the bottom of the cube, and 1 moving up to the top face. As you can see, if we pick the leftward path we force the other two colors to block each other. So, from the remaining option we have to block check to keep top-2 clear. Now the solution is clear. Fill top-2. Loop left-1. And the rest is linear.
• 16: If this is the first level that really stumped you, there's a good reason why. With 75 squares to consider and 6 colors, just trying to flag or block check can be overwhelming. When a solution isn't in sight, we have to use our techniques to make things as easy as possible. When drawing flags, it's probably best to draw the path of least resistance. So, starting on the perimeter and working around the sides is a good way to start. Or starting in the center and keeping things compact. In this case, I started with left-3 and flagged 2 paths wrapping around the whole cube. Then I picked left-2 and did the same. When I reached the end of this line, I had to overwrite a previously made line. This is great. The method chose which direction (left or right) was best for left-3. Then I connected left-1 going downward to avoid cutting off the path of right-4. From there I kept the lines of top-3&4 compact. At this point I realized that I was going down the wrong path. But, double reading the game state, I saw that by making one adjustment, all the other lines were forced into a new formation in a sort of chain reaction. Adjust each line at least once (even the first line we made) and the solution becomes linear. 

If you're interested enough and motivated enough to at least play 3D logic, do tell me what your experience was like. I may log in solutions for the rest of the levels, but I think 16 is enough to communicate my point. If you underestimated the potential difficulty on the early levels, you may have held yourself back from developing the techniques necessary to beat the game. Anyone can randomly stumble onto the solution with enough trail and error. But devising a solid methodology and being able to communicate/teach it is definitely on a higher level of cognitive skills. 

If you only realized that your old methods of finding solutions is essentially random attempts or rolling the dice, then remember this moment. That's what it feels like to move from unintuitive to Eureka. 

Comments

[metastase]

Started level 1 with 1 rule in mind: to start each game by looking out for blocks with 3 spaces blocked around them then filling in the only move possible. After some levels, I kept a mental note to myself to look out for situations when filling 1 obvious move would force more filling elsewhere. Note that this is the only actual filling I did in the game until I mentally solved the whole level.

At some point, I started defaulting to 2 major considerations after the obvious moves mentioned above: to mentally trace the "longest/most far away line/block of least resistance/non crossing" while simultaneously "mentally connecting the closest lines/blocks that aren't crossing the path of other ones". As a plus, the 1st ones I would glance were the ones with the least amount of "exits" (like only 2 possible exits from the starting block, then only consider 3 and 4 exits later on if needed which I don't even know if actually happened).

If the result after considering those still included non obvious lines with crossing paths, I started looking for the best "worm-like line". I think this is what you call "loops". Finding this line usually resolved everything else instantly.

I don't even remember what level 16 was like and everything flew by pretty fast. It's hard to gauge the actual order by which I applied those considerations above, I know for a fact that sometimes I would do them out of order (like finding the worm-like line 1st even though looking for obvious filling should have been my 1st move).

I suspect I just understood intuitively by looking at some configurations that sometimes it would be easier to solve the whole puzzle by simply "finding" the worm-like line. When I spotted lots of crossing lines, it was like "Y'know what? I'm not gonna bother to mentally trace those lines" so due to lazyness sometimes I intuitivelly looked for loops 1st and see if they resolved a whole bunch of lines, which is exactly what happened most of the time.

A couple times a string of 5~8 levels were solved like if I already knew the solution (in a matter of seconds), I would look at the cube and start filling without much complication or problems. Most of the time I would solve 2~3 levels really fast, then take some time looking at the cube for 1 level, then repeat a short burst of quick levels, etc.

Because everything was going really fast, at around level 25 I remember feeling excited but also dreading the later levels, thinking to myself "Man, I think I'm going to be stuck before half-way through". At this point, I thought the game had something like 100 levels (so I was wondering if I could break through level 50 without being stuck).

I kept repeating the above until I had great difficulty at level 28. For some reason, I just couldn't see which worm-like line solved the level. It took me more than 10 minutes to solve this one. Part of the problem is because I couldn't determine which one should be the "longest/most far away line of least resistance/non cross over paths" and the fact that the center was cluttered to the point that most lines where close together so mentally tracing the short lines didn't help any. So I needed a new strategy.

My "void" strategy to reduce the complexity even further for this level: I counted how many "passages" where free from each plane into every other plane. For example, like 2 possible paths from what you call Left to Top, 1 from Top to Right, 2 from Right to Left, etc (not actual numbers, this is just example). From this, I decided which line should NOT go into any given direction due to crossing paths (so if 1 path blocked out other 2 and the remaining possible paths for them were less than 2 or permanently blocked out a path for yet other lines, I would know 100% that they were wrong).

However, the whole point of it was to help determine the correct loop and not to find their actual correct lines (although I instantly found one when my strategy shifted to this: IIRC, I instantly determined the bottom-rightmost line from the Right should go down and not any other way).

After looking at the cube for while with this in mind, I could see the worm-like line I was missing (and then understood why I missed it): it was 1 center line that indeed crossed 3 paths stringed together which is probably why I was hesitant to even consider it as the possible loop line (I mean, what are the odds of the correct path being one crossing 3 blocks right in their faces? lol). Not only that, it turned out to be a double loop line crossing another one beyond those 3.

Then I solved the last few levels in about 30 seconds and thought "What? It's over?".

You see, my surprise was because I usually suck at puzzles. I was sure it would come to a point where each sequential level would get me stuck like level 28 but a string of 2 longer levels never happened. I don't know why and I find this to be very strange. Also, I remember thinking to myself after level 28 "I think I'll need to develop a new strategy involving actually painting some lines instead of just looking/mentally solving the puzzles real soon or I'm sure I'll be stuck later on" but it was never needed, so this became an after thought.

As a side note, I don't really like puzzle games. The only reason I did this one is because I was curious if it would give me some sort of insight into the whole Eureka thing you were talking about. Well, it didn't. To be fair, it didn't because I personally feel that this whole Eureka series of articles didn't satisfy me. The reason, I think, is probably because I disagree with your conclusion. Or rather, the ending tone didn't feel right because I know from personal experiences that what you call "trial and error" can't be easily dismissed as just that, as you imply.

IMO, you didn't consider the possibility that the motivation behind trial and error behavior can also be strategic in nature. Other times, deeper strategies can only flourish after trial and error was the 1st step. How do you determine which move is the best at any given time in a fighting game? There's no way around this, the 1st step is trial and error because you need to know the moves before anything else.

My highest point of divergence with your thoughts on this is probably that I don't think trial and error are random attempts like rolling a dice at all. At its worse, it's always teaching and updating which gameplay verbs are the most practical given the context you're using them in. To make an analogy, they're like the 1st character build you make in an MMORPG. No matter what you do or how much you read about the game upfront, that 1st character experience will involve lots of mistakes. You'll probably mess up the character build. And probably sell valuable items to NPC for low profit when you should have sold them to players. It will probably suck at PVP too.

But all of this trial and error gives you the knowledge you need to make a decent character the 2nd time around.

I guess the bullet point of my conclusion is: I'm surprised someone interested in how we learn by carefully observing how we play games can simply overlook trial and error. The implication being, it can't be purged from consideration just for some arguments sake.