Whether all questions must be solved depends entirely on the context. There's no universal rule that applies to all situations.

• In a graded exam: Usually, not all questions must be answered correctly to pass. Partial credit and different grading scales exist.
• In research: Some research questions might remain unsolved for extended periods or indefinitely.
• In everyday life: Many questions we encounter might not have definitive answers or require a solution.

The requirement to solve all questions is specific to the situation and its objectives.