Knight's Tour

The concept of a tour can be described as a journey undertaken by an entity to travel sequentially from one place to another. They may or may not return to the point of origin. In the context of chess, the knight moves in an L shape using 3 steps in any of the four directions.

What if one combined or blended these two concepts? That is how the knights tour came to be - A puzzle that utilizes the moves of a knight to tour the chess board under certain constraints. The constraints include not traversing the same square more than once, and (not necessarily) that it has to return to its point of origin.

When approaching the Knight’s Tour puzzle, one might end up discovering two kinds of paths - open and closed. An open path refers to a tour where the knight does not return to its point of origin, whereas a closed one involves the knight returning to its point of origin. There are multiple satisfiers and many ways to figure out the solution to this problem.

One of the satisfier involves decomposing (or breaking down) the grid into 4 modular parts (2 parts of 4x3 and 2 parts of 5x4). And because of its modular nature, one needs to figure out the pattern of just 2 of the 4 parts and mirror the pattern on the rest.