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Problem Solving — Definition & Types

📊 Topic Overview​

| Papers Appeared | 14/28 (50.0%) | | Priority | 🔴 HIGH | | Session Split | Equal (7 June / 7 December) | | Often Combined With | Problem Solving Strategies |

🎯 Must-Know Concepts​

  1. Definition of problem — initial state, goal state, obstacles
  2. Well-defined vs Ill-defined problems
  3. Types of problems — arrangement, transformation, inducing structure
  4. Problem space (Newell & Simon) — states and operators
  5. Routine vs Non-routine problems
  6. Convergent vs Divergent problems
  7. Insight problems — sudden restructuring (Gestalt)

Previous Year Questions​

Year-SessionQuestionMarks
2011-JuneDefine and explain the nature of problems10
2013-JuneDiscuss the nature and types of problems10
2014-JuneDescribe the types of problems in problem solving10
2016-DecemberExplain the nature of problem solving10
2017-JuneTypes of problems (B section)6
2019-JuneDiscuss the nature and types of problems10
2021-JuneExplain the definition and types of problems10
2022-DecemberShort note: Types of problems3
2024-JuneDiscuss the nature of problem solving10

🌟 Comprehensive Answer: Problem Solving — Definition & Types (~500 words)​

Introduction​

Problem solving is one of the most fundamental and extensively studied domains of cognitive psychology. It refers to the cognitive process of moving from a current state to a desired goal state when the path is not immediately obvious. Problem solving involves recognising that a problem exists, understanding its nature, generating possible solutions, evaluating them, and implementing the best solution. It is central to human intelligence and adaptive behaviour.

Definition of a Problem​

A problem exists when there is:

  1. A current (initial) state — the present situation
  2. A goal state — the desired outcome
  3. Obstacles — barriers preventing direct movement from initial to goal state
  4. Operators — actions available to transform states

Newell and Simon (1972) formalised this as the Problem Space — the set of all possible states that could exist between the initial state and the goal state, plus the operators that move between states.

Well-Defined vs Ill-Defined Problems​

TypeCharacteristicsExamples
Well-definedClear initial state, clear goal, clear operatorsSolving a maths equation, chess
Ill-definedVague initial or goal state, unclear constraintsWriting a poem, designing a building, life decisions

Most real-world problems are ill-defined — they require the problem solver to first define the problem before solving it.

Types of Problems​

Greeno (1978) classified problems into three main types:

1. Problems of Arrangement​

Rearranging elements to satisfy some criterion:

  • Anagrams: Rearranging letters to form a word (e.g., RCBKI → BRICK)
  • String problems: Attaching strings in a room (Maier, 1931)
  • Often solved through trial-and-error or insight

2. Problems of Inducing Structure​

Identifying the relationship between elements and extending it:

  • Analogy problems: A:B :: C:? (e.g., Doctor:Hospital :: Teacher:?)
  • Series completion: 2, 4, 6, 8, ?
  • Require identifying the underlying rule or pattern

3. Problems of Transformation​

Changing an initial state into a goal state through a sequence of moves/operations:

  • Tower of Hanoi: Move discs from one peg to another following rules
  • Hobbits & Orcs (missionaries & cannibals): Move characters across a river
  • Require planning sequences of operations

Additional Classification​

CategoryDescription
Routine problemsPreviously practised; solved by applying known procedures
Non-routine problemsRequire novel approaches; no known algorithm
Insight problemsSolved through sudden restructuring (Gestalt "Aha!" experience)
Convergent problemsOne correct answer (e.g., maths)
Divergent problemsMultiple possible answers (e.g., brainstorming)

Insight vs Non-Insight Problems​

Gestalt psychologists (Wertheimer, Köhler, Duncker) highlighted insight — the sudden realisation of a solution through perceptual restructuring of the problem. Köhler's famous experiments with Sultan the chimpanzee showed insight in animals. Insight problems often involve overcoming functional fixedness (inability to see novel uses for familiar objects).

Conclusion​

Understanding the definition and types of problems is foundational to studying problem solving. Problems vary enormously — from well-defined mathematical puzzles to ill-defined real-world challenges — and different types require different cognitive strategies. The problem-space framework of Newell and Simon provides a unifying representation, while Greeno's classification identifies the specific demands of arrangement, induction, and transformation tasks.

🧠 Memory Aid​

"AIT" = Arrangement, Inducing Structure, Transformation
"A good AI Thinks in all three ways"

Well vs Ill defined: "Chess is Well-defined, Life is Ill-defined"

📚 Related Content​

✅ Self-Assessment​

  1. Define a problem using the concepts of initial state, goal state, and obstacles.
  2. What is the difference between well-defined and ill-defined problems?
  3. What are Greeno's three types of problems? Give an example of each.
  4. What is an insight problem? How does it differ from a routine problem?
  5. What is functional fixedness?

💡 Exam Tips​

  • Start with Newell & Simon's problem space definition
  • Greeno's 3 types are essential — always include with examples
  • For 6-mark: 3 types + brief definition each
  • For 10-mark: definition + problem space + well/ill-defined + all 3 types + insight mention
  • Tower of Hanoi and anagrams are go-to examples for transformation and arrangement