Cognitive subject imposes structures on an object to shape it into a structured thing. Structures that the subject imposes on an object in a given problem context can be diverse horizontally and vertically. In view of the horizontal diversity of structure, problem-solving activities focusing on various structures may enrich the present problem-solving education which emphasizes applying and comparing a couple of problem-solving strategies. Finding an algebraic formula for a figural pattern should be regarded as a new starting point of searching for more various structures. In view of the vertical diversity of structure, it should be aware that students may see different structures from the structure that their teacher expect them to see. The vertical diversity of structure enables us to provide students with experience of progress.