2 Problem-Solving Strategies

Represent the problem

Problem solving means moving from a present situation to a desired outcome when the steps are not immediately obvious. Which strategy is effective depends on how clearly the problem is defined, what information and actions are available, and how much time or certainty the solution requires.

Begin by creating a useful problem representation: identify the starting state, the goal, relevant constraints, and possible actions. A helpful representation can make a solution easier to see, while an unhelpful one can make a solvable problem seem difficult.

Choose a strategy

Choose a strategy based on the problem’s definition, available resources, and need for speed or certainty.

• Algorithm: Follow a defined sequence of steps. This suits well-defined problems with a known procedure, such as a standard calculation or checklist. It can be slow or impractical when many possibilities must be checked, and a suitable procedure may not be known. When an algorithm is complete and correctly applied to a problem it covers, it can guarantee a solution.

• Heuristic: Use a practical rule of thumb to guide the search. This suits problems with limited time or information, or too many possible paths for exhaustive search. It is usually faster, but can lead to an incorrect answer; check the result when accuracy matters.

• Means–ends analysis: Compare the current state with the goal and select actions that reduce the difference, creating subgoals when necessary. It suits multi-step problems where progress can be described as reducing specific gaps. An action that seems to reduce one gap may create another or lead to a dead end.

• Trial and error: Test possible actions and use the outcomes to guide the next attempt. This suits small search spaces, low-cost experiments, or situations with quick feedback. Unplanned repetition wastes time and may repeat failed attempts.

In general, use an algorithm when the problem is well-defined and correctness is important. Use a heuristic when speed or flexibility matters more, while checking its result if the stakes are high.

Apply means–ends analysis

Means–ends analysis treats problem solving as a search through possible states. Compare the present state with the desired state, identify a difference, and choose an action that may reduce it. If the action cannot be taken yet, set a subgoal to remove the obstacle; repeat until the goal is reached, then verify that the result meets the original requirements.

For example, the goal may be to deliver a printed report by the end of the day. The report is finished, but the printer does not work, so there is no usable printed copy. Possible actions include checking the connection, paper, and ink. If the printer still fails, a subgoal could be finding another printer; printing at a nearby library or asking a colleague may then reduce the remaining gap. Consider constraints such as travel time and the deadline before choosing.

Use additional approaches

Several other approaches can help, depending on the structure of the task.

• Break the task into subgoals: Turn a broad objective into manageable steps and track which are complete. This is useful for projects and other tasks with several stages.

• Work backward: Start with the required endpoint and ask what must happen immediately before it. Continue backward until reaching the present. For example, to arrive by a fixed time, estimate travel time and work back to a departure time. This is especially useful when the goal and the steps leading to it are clear.

• Use analogy: Recall a previous problem with a similar underlying structure and adapt its solution. Check that the important constraints match; surface resemblance alone can mislead.

• Use controlled trial and error: Change one relevant factor at a time, record what you tried, and use each outcome as information. This makes testing more informative than repeating guesses.

• Pause and reframe: If progress stalls, a brief break or a new description of the problem can reveal a different approach. Insight may feel sudden, but check the solution against the problem’s rules.

Recognize and address barriers

Mental set—persisting with a familiar method after it stops working—and functional fixedness—seeing an object only in its usual role—can both narrow the solutions considered.

To respond, restate the goal and constraints in plain language, distinguish essential rules from assumptions, and deliberately generate an alternative representation or method. If attempts repeatedly fail, stop repeating them: identify what each attempt taught you, reconsider the starting conditions, and choose a different strategy. Finally, test the proposed solution against the goal and constraints, not just whether it seems plausible.