Generating diverse solutions is key to human-like reasoning, yet autoregressive language models focus on single accurate responses, limiting creativity. GFlowNets optimize solution generation as a flow network, promising greater diversity. Our case study shows their limited zero-shot transferability by fine-tuning small and medium-sized large language models on the Game of 24 and testing them on the Game of 42 datasets. Results revealed that GFlowNets struggle to maintain solution diversity and accuracy, highlighting key limitations in their cross-task generalization and the need for future research in improved transfer learning capabilities.