# Applications of Algorithms¶

Hactar, 2024-04-15

Neophyte Cherto toiled into the late hours of the night, eager to complete their latest assignment: producing a written guide to their own solution to Rubik’s Puzzle of Four Dimensions. They had solved the puzzle once before, but Master Nazir had suggested that they solve it again before beginning their writing, for there was a case they had not yet encountered.

As Cherto approached the end of the Orientation of the Last Cell of their 3x3x3x3, they found that only a single piece was twisted in place. Cherto, being wise in the ways of Isolation and the construction of Commutators, was easily able to solve this case. They carefully noted the sequence of moves they had performed, added it to their guide, and then continued on.

Some days later, another disciple came upon Cherto and addressed them. “I am Neophyte Nima. I have nearly solved my puzzle, save for a single 3-color piece twisted in place. Its stickers are permuted in a cycle, and I cannot seem to rotate it without rotating another piece. Master Nazir said that you had recently solved this case and suggested that I learn from the solution from you.”

Cherto excitedly withdrew the latest draft of their solution guide and began copying their algorithm onto a slip of parchment for Nima to read. They began: U R2 ...

Later that day, Master Nazir found Nima still struggling on the same monotwist case, and inquired whether she had found help from Cherto. She replied: “Cherto was kind enough to provide their method, but I believe they copied it wrong, for my puzzle becomes scrambled when I apply their algorithm!”

“Cherto has given you an algorithm?” Master Nazir peered over her shoulder. “I see you struggle with the application of Cherto’s algorithm. Did they explain the derivation of this algorithm to you?” Nima responded that they had not. Master Nazir left the room, leaving Nima to her struggles.

Shortly after, Master Nazir returned with Neophyte Cherto. Cherto watched Nima diligently applying their algorithm to the hemimegaminx in front of her, unaware of its origins.

At that moment, Cherto was enlightened.