This paper presents three facets of HANAGRAM: Math Puzzle, Art Puzzle, and Puzzle Art. HANAGRAM, invented by the author in 2022, offers a unique combination of logical thinking and art thinking. Logical thinking puzzles involve Number-Fill-in puzzles, akin to the popular Sudoku. Art thinking puzzles, on the other hand, focus on image appreciation by interpreting and naming the figures created through coloring. In this paper, I will share the journey of how I created HANAGRAM and developed it from a puzzle into a form of art, from the perspective of a puzzle creator.