Of three men, one man always tells the truth, one always tells lies, and one answers yes or no randomly. Each man knows which man is which. You may ask three yes/no questions to determine who is who. If you ask the same question to more than one person you must count it as a question used for each person asked. What three questions should you ask?

The 'truth-tellers and liars' puzzle is a classic example of a logical conundrum that requires careful analysis and critical thinking to solve. Imagine a scenario where you encounter three individuals—each with distinct behavioral patterns regarding truthfulness. One person always tells the truth, another always lies, and the third provides answers at random.

When tackling this kind of puzzle, your goal is to determine the identity of each person based on their responses to yes/no questions. To achieve this, it's pivotal to craft questions strategically to reveal inconsistencies or certainties in their responses. For instance, if you ask the individual who lies whether another individual always tells the truth, the response will surely contradict the actual truth. Similarly, the truth-teller would provide a response that accurately reflects reality. The random responder adds complexity since their replies cannot be relied upon.

The key strategy lies in asking questions that are self-referential or about the other individuals, as these can provide indirect information that aids in identifying who's who. The questions should be constructed to deliver information no matter who is answering. This ensures that you systematically eliminate the impossibilities to arrive at the one possible truth.

Deductive reasoning is a fundamental method in logic and problem-solving that involves drawing specific conclusions from general premises or known facts. This logical process starts with a theory, narrows down to observations, and leads to a confirmation.

In the context of truth-tellers and liars puzzles, deductive reasoning is used to analyze the implications of each person's answers to the yes/no questions. Each response provides information that helps in deducing the roles of the individuals. For example, if person A, when asked about person B, indicates that B is a truth-teller, and we know that at least one of them is not, we can begin to deduce who is lying based on the structure of the puzzle. It's important to understand that deductive reasoning is only as accurate as the premises it starts with—in this case, the consistency of behavior (truth-telling, lying, random) of each individual.

Furthermore, deductive reasoning allows for a rigorous approach to problem-solving, where each step or conclusion is based on the logical implications of the previous steps or established facts. By employing deductive reasoning, you can ensure the conclusions drawn are valid and reliable, provided that the initial statements are correct.

Problem-solving strategies are diverse techniques used to address challenges and find solutions. These strategies can vary from straightforward trial and error to complex algorithms or heuristics. When solving logical reasoning puzzles, there are several strategies that can be particularly effective.

Firstly, breaking down the problem into smaller parts can help manage complexity, making it easier to handle one aspect at a time. In truth-tellers and liars puzzles, this means dealing with the answers of one person before moving onto the next.

Another important strategy is looking for patterns or invariants—elements that do not change despite different scenarios. This might include the consistent behavior of the individuals in the puzzle, regardless of the specific questions asked.

Also, using process of elimination to weed out impossibilities helps narrow down the range of possible solutions. By methodically eliminating scenarios that cannot be true, given the constraints of the problem, you can hone in on the correct answer with greater precision.

Moreover, approaching the problem with an open mind and being willing to backtrack and reassess your logic when faced with new information is crucial. As highlighted by the step-by-step solution, asking the right series of questions and analyzing the responses based on previous answers is key to solving the puzzle. Effective problem-solving in such puzzles involves both creative thinking to devise the right questions and logical rigor to interpret the answers correctly.