Background: Empirical studies have revealed students' development of computational thinking (CT) and mathematical thinking (MT) during programming-based mathematical problem-solving, highlighting specific CT concepts or practices that serve as learning goals or outcomes. However, implementing programming-based mathematics instruction requires teachers to have sufficient knowledge about learners' thinking processes in such a context, while very little is known about multifaceted solution development from a learner-centred perspective. Objectives: Viewing CT and MT as processes that go beyond specific skills or concepts, we conducted a qualitative study to investigate how participants develop computational solutions to mathematical problems and construct meaningful understandings of these solutions. Methods: We adopted an interpretive approach to participants' solution pathways to reveal their diverse thinking processes underlying solution development. A constant comparative analysis approach was undertaken to guide the data analysis. Results and Conclusions: We identified multiple solution pathways in developing programming-based mathematical solutions (PMS) and characterised four significant pathways comprising seven distinct sub-situations: (1) transition between personal MT and invalid PMS, (2) evolution from invalid PMS to valid PMS, (3) construction from non-meaningful PMS to meaningful PMS and (4) revision from suboptimal PMS to optimal PMS. The findings contribute to a deeper understanding of problem solvers' learning in programming-based mathematical problem-solving and offer implications for theory and practice in programming-rich mathematics education.