Large Language Models (LLMs) excel in reasoning tasks requiring a single correct answer, but they perform poorly in multi-solution tasks that require generating comprehensive and diverse answers. We attribute this limitation to \textbf{reasoning overconfidence}: a tendency to express undue certainty in an incomplete solution set. To examine the effect, we introduce \textit{MuSoBench}, a benchmark of multi-solution problems. Experiments show that the conventional short chain-of-thought (Short-CoT) prompting paradigm exhibits pronounced overconfidence, whereas the emerging long chain-of-thought (Long-CoT) approach mitigates it through iterative exploration and self-reflection. We further characterise observable behaviours and influential factors. To probe the underlying cause, we propose the \textbf{cognitive-rigidity hypothesis}, which posits that overconfidence arises when the reasoning process prematurely converges on a narrow set of thought paths. An attention-entropy analysis offers preliminary support for this view. These findings provide tools for assessing the completeness of LLM reasoning and highlight the need to move evaluation beyond single-answer accuracy toward comprehensive exploration.