Which type of thinking promotes expanding the number of possible solutions to a problem?

Divergent thinking is the type of thinking that promotes expanding the number of possible solutions to a problem. This cognitive process encourages the generation of multiple, varied concepts, ideas, or perspectives. The essence of divergent thinking lies in its ability to explore numerous avenues and options, often seen in brainstorming sessions where quantity of ideas is prioritized over the immediate quality or feasibility of those ideas.

In contrast, convergent thinking focuses on narrowing down multiple solutions to find the singular best answer or solution, working towards a definitive conclusion. Creative thinking often overlaps with divergent thought but can encompass both the generation of new ideas and the refinement of existing concepts. Analytical thinking is more about breaking down complex information into manageable parts to assess and understand it better, not necessarily generating multiple solutions.

Thus, divergent thinking distinctively supports the exploration of many possibilities, which makes it the correct choice in this context.