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.