This paper introduces a novel and significant challenge for Vision Language Models (VLMs), termed Unsolvable Problem Detection (UPD). UPD examines the VLM's ability to withhold answers when faced with unsolvable problems in the context of Visual Question Answering (VQA) tasks. UPD encompasses three distinct settings: Absent Answer Detection (AAD), Incompatible Answer Set Detection (IASD), and Incompatible Visual Question Detection (IVQD). To deeply investigate the UPD problem, extensive experiments indicate that most VLMs, including GPT-4V and LLaVA-Next-34B, struggle with our benchmarks to varying extents, highlighting significant room for the improvements. To address UPD, we explore both training-free and training-based solutions, offering new insights into their effectiveness and limitations. We hope our insights, together with future efforts within the proposed UPD settings, will enhance the broader understanding and development of more practical and reliable VLMs.

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