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Problem Solving — Strategies & Techniques

📊 Topic Overview​

MetricValue
Papers Appeared27/28 (96.4%)
Total Questions29
Priority🔴 HIGHEST — Most consistent topic across all years
Section DistributionSection A, B, and C
Years AppearedEvery year (2011–2024)
Most Consistent Topic

Problem Solving Strategies appears in 27 of 28 papers — effectively every single exam. It is impossible to predict MPC-001 without knowing this topic.

🎯 Must-Know Concepts​

  1. Stages of problem solving — Polya (1945) or Bransford & Stein (IDEAL model)
  2. Algorithms — systematic exhaustive procedures
  3. Heuristics — rule-of-thumb strategies (means-ends analysis, working backward, hill climbing, analogical reasoning)
  4. Specific techniques — brainstorming, SCAMPER, synectics, lateral thinking
  5. Trial and error
  6. Insight vs analytical problem solving
  7. Difference between well-defined and ill-defined problems

📝 All Previous Year Questions​

Year-SessionQuestionMarks
2011-DecemberDiscuss strategies for problem solving10
2012-JuneDiscuss strategies of problem solving10
2013-DecemberDiscuss strategies and stages of problem solving10
2018-JuneDiscuss stages and strategies of problem solving10
2018-DecemberExplain strategies of problem solving10
2019-DecemberExplain strategies of problem solving10
2020-DecemberDiscuss strategies and techniques of problem solving10
2022-JuneDiscuss stages and strategies of problem solving10
2022-DecemberDiscuss stages and strategies of problem solving10
2023-DecemberDiscuss specific techniques of problem solving10
2024-DecemberDiscuss techniques in problem solving10
(Plus many Section B and C appearances in other years)

🌟 Comprehensive Answer: Strategies & Techniques of Problem Solving (~500 words)​

Introduction​

Problem solving is the cognitive process of moving from an initial state to a goal state when the path is not immediately obvious. Effective problem solving requires not only subject matter knowledge but also a repertoire of strategies — general approaches applicable across problem types — and specific techniques — methods tailored to particular problem domains.

Psychologists have identified both algorithmic and heuristic strategies, as well as a range of creative techniques that support problem solving in complex, ill-defined situations.

Stages of Problem Solving​

Before strategies can be applied, problems must be approached systematically. Polya (1945) proposed four stages in his classic text How to Solve It:

  1. Understand the problem: What is given? What is unknown? What are the constraints?
  2. Devise a plan: Select a strategy — can you use a related problem? Break it into parts?
  3. Carry out the plan: Execute the strategy carefully, checking each step.
  4. Look back / Review: Verify the result. Can you derive it differently? Can you use this approach for other problems?

The IDEAL model (Bransford & Stein, 1984) offers a similar framework:

  • Identify the problem
  • Define and represent the problem
  • Explore possible strategies
  • Act on the strategies
  • Look back and evaluate the effects

Types of Problem-Solving Strategies​

1. Trial and Error The most basic strategy — trying possible solutions randomly or systematically until one works. Effective only for simple problems with limited solution spaces. Time-consuming and inefficient for complex problems.

2. Algorithms An algorithm is a step-by-step procedure that guarantees a correct solution if followed correctly. Examples: long division, solving simultaneous equations, following a recipe. Algorithms are reliable but can be time-consuming when the problem space is large (e.g., checking all possible chess moves).

3. Heuristics Heuristics are mental shortcuts or rules of thumb that reduce the problem space and make problem solving more efficient — but do not guarantee a correct solution. Major heuristics include:

  • Means-Ends Analysis (Newell & Simon, 1972): Identify the difference between the current state and goal state; apply operators that reduce this difference. Decompose the problem into sub-goals. This is the basis of the General Problem Solver (GPS).

  • Working Backward: Start from the goal state and work backward to the initial state. Useful when the goal is clearly defined but the starting path is unclear (e.g., geometric proofs, planning a route).

  • Hill Climbing: At each step, move in the direction that brings you closer to the goal — always choosing the locally best option. Simple but can lead to local maxima (stuck in a suboptimal position).

  • Analogical Reasoning: Use a known solution from a similar problem as a template. Duncker's radiation problem is a classic example where the military analogy (converge forces from multiple directions) solves the medical problem (converge multiple weak radiation beams).

  • Subgoal Decomposition: Break the main problem into smaller, manageable sub-problems. Each sub-goal is solved independently, with solutions combined for the final answer.

Specific Problem-Solving Techniques​

1. Brainstorming (Osborn, 1953) A group or individual technique for generating a large number of ideas without evaluation or criticism. Rules: (1) quantity over quality, (2) no criticism during generation, (3) build on others' ideas, (4) wild ideas welcome. The evaluation phase comes afterward.

2. Lateral Thinking (de Bono, 1967) A deliberate approach to thinking that challenges assumptions and looks at problems from unexpected angles. Rather than "digging deeper" in the same direction (vertical thinking), lateral thinking involves moving sideways — restructuring the problem itself. De Bono's techniques include random input (introducing an unrelated concept to spark new connections) and the Six Thinking Hats method.

3. Synectics (Gordon, 1961) Uses four types of analogies to transform a familiar problem into something unfamiliar (and vice versa), enabling fresh perspectives: (1) Direct analogy — compare to another real-world process; (2) Personal analogy — imagine being the problem; (3) Symbolic analogy — compressed, poetic description of the problem; (4) Fantasy analogy — ideal solution unconstrained by reality.

4. SCAMPER A checklist technique for creative problem solving:

  • Substitute — what can be substituted?
  • Combine — can elements be combined?
  • Adapt — what can be adapted from elsewhere?
  • Modify / Magnify / Minify — how can it be changed in size or form?
  • Put to other uses — other applications?
  • Eliminate — what can be removed?
  • Reverse / Rearrange — what if reversed or reordered?

5. Insight Problem Solving Some problems are solved through insight — a sudden restructuring of the problem representation leading to the solution. Unlike analytical strategies, insight feels sudden and discontinuous. Associated with the "Aha!" experience. Gestalt psychologists (Köhler, Duncker, Wertheimer) studied insight extensively. Modern research (Bowden & Jung-Beeman, 2003) links insight to right temporal lobe activity.

Conclusion​

Effective problem solving draws on multiple strategies simultaneously. Experts in any domain have automated relevant algorithms and have a richer repertoire of appropriate heuristics — leaving more cognitive resources for novel aspects of the problem. Training in problem-solving strategies is therefore valuable across academic and professional contexts. The interplay between algorithmic precision, heuristic efficiency, and creative restructuring defines expert problem solving.

Related Content:

📝 Section B Answer: Stages and Strategies (~300 words)​

For 6-mark questions on stages and strategies

Problem solving involves moving from an initial state to a goal state. This process typically follows identifiable stages:

Polya's (1945) four stages are: (1) Understanding the problem — identifying what is given, what is required, and constraints; (2) Devising a plan — selecting an appropriate strategy; (3) Carrying out the plan — implementing the chosen strategy carefully; (4) Looking back — evaluating the solution and generalizing the approach.

Strategies used within these stages include:

Algorithms — guaranteed step-by-step procedures (e.g., mathematical formulae). Reliable but computationally expensive.

Heuristics — efficient rule-of-thumb shortcuts: means-ends analysis (reduce the gap between current and goal state), working backward (start from goal), analogy (map a familiar solution onto the new problem), and subgoal decomposition (break into smaller problems).

Insight — sudden restructuring of the problem representation, the "Aha!" moment, not explainable by systematic strategy alone.

Effective problem solvers use algorithms where precision is required, heuristics to reduce search space, and insight-fostering environments (incubation, analogies) for creative problems.

🧠 Memory Aids​

IDEAL stages: Identify, Define, Explore, Act, Look back

Heuristics — "MWHAS": Means-ends, Working backward, Hill climbing, Analogical, Subgoal

SCAMPER: Substitute, Combine, Adapt, Modify, Put to uses, Eliminate, Reverse

✅ Self-Assessment​

  1. What is the difference between an algorithm and a heuristic?
  2. Describe means-ends analysis with an example.
  3. What is brainstorming? What are its four rules?
  4. How does lateral thinking differ from ordinary problem solving?
  5. Describe Polya's four stages of problem solving.