Strange Color Patterns
When I was a freshman in high school, I befriended a senior in my math class. I was hanging with her and a few of her friends, one of whom was doing a Rubik's cube. I started messing around with it, and I could get one face a solid color. So he taught me the few other moves to get to a solution.
I still couldn't solve it. I think he gave me an old Rubik's cube, and I practiced non-stop for the next few days before I finally solved it once. I was even playing with it in class. I could not focus on anything but solving this cube. Then I was able to solve it a few more times, and then I could solve it all the time.
This method is not the fastest, but it will always work. The fastest currently is 4.22 seconds. In 1999, when I learned how to do it, the record was 17 seconds which had been the record for 17 years. There are mathematicians who showed you could solve it in so many moves. I remember it being around 26 when I started, and at some point, people ran simulations of all possible starting positions to show that 20 was the absolute maximum.
The method I use takes a long time, and even at my fastest, I could only finish in just under two minutes. I wasn't bothered by this. I used to solve it so often, I only had to glance at the cube. It turned into a fidget spinner before there were fidget spinners. It was a calming experience and a fun party trick.
The fun part came in determining math related combinations. It is easy to make a checkered board cube where each side had two colors, with zero connectivity between colors. 4-connectivity is when two same-colored squares touch side-by-side, and 8-connectivity is when two same-colored squares touch side-by-side or corner-by-corner. 0 connectivity means colors are surrounded on all sides and corners by different colors.
Two different colors is simple to achieve. Three different colors didn't interest me. Four colors was straight forward. Five colors was another ballpark. I figured out that five colors could be achieved by flipping each piece around each axis. I had to visualize what this would look like, and I imagined the pattern as I tried to solve it. I figured it out.
Six colors on each side was very interesting. Initially, I figured it was a modification to five colors, and I worked it out the long way. The long way being that you have to flip each square on all three axes. Then I found a very short path to get to it while I was messing around with the cube. I was simply trying to mix it up in an organized fashion. This method though still has corner pieces connected (8-connected) but only requires 12 half-turns.
The Rubik's cube kept my attention for a long time, and I can still solve it. I'm not sure what fascinates me more, the puzzle, the sound the cube makes, or just the pretty colors.