"Solution Path": The structure of the solution steps for pencil puzzle

Many puzzles can be solved as a state-space search problem. On the other hand, pencil puzzles such as Number place or Kakkuro are usually solved in the deterministic way by inferring without branching and backtracking. The key is the sequence of selecting a part of solution. We propose a new model of solution structure for pencil puzzle, where all the possible sequences are combined in the lattice. We focus on the sequences of the solution process, and propose the concept of solution path. The structure that shows the solving process is based on this concept. We get the solution paths from pencil puzzle and conjecture the situation of that problem. We take up the example of Kakkuro´s problem. We get the solution paths and then show the feature of situation on the human thought process.