Solving Real-World Problems

Most of what we practise in school looks like a puzzle: a clear starting point, a clear goal, and rules that tell you when you are right. Most of what we face in life does not. "Choose a career," "fix this team," "grow the business" — these arrive without a stated goal, without all the facts, and without an answer key.

When you treat a messy real problem as if it were a puzzle, you tend to seize the first clear goal you can name and race toward it, only to find you solved the wrong thing. Recognising which kind of problem you have changes the whole approach — from finding the answer to constructing a workable one.

Well-defined versus ill-structured

Cognitive scientists have long distinguished well-defined problems from ill-defined or ill-structured ones. A well-defined problem has a clear initial state, a clear goal, and a known set of legal moves — a Sudoku, a chess endgame, a maths exercise. An ill-structured problem, described by Walter Reitman in 1964 and analysed by Herbert Simon in his 1973 paper "The Structure of Ill-Structured Problems," is missing one or more of those: the goal is vague, the information is incomplete, the operators are unclear, or there is no agreed test for a good solution.

Why real problems are messy

Three gaps recur. First, unclear goals: "be happier" or "improve the product" does not say what success looks like. Second, missing information: you rarely have all the facts, and gathering more costs time. Third, no single right answer: several solutions may be defensible, judged better-or-worse by people who weigh things differently. Simon argued the line between well- and ill-structured is not absolute — part of solving is converting a fuzzy problem into a series of better-defined sub-problems you can actually work on.

How the mind copes

Because we cannot compute the perfect answer to an open problem, we satisfice — Simon's term for accepting an option that is good enough against our criteria rather than searching endlessly for the best. We also lean on reframing, gathering just enough information to reduce the worst uncertainty, and taking small reversible steps that teach us more about the problem as we go.

Suppose your goal is "improve customer retention." As stated, it is ill-structured: retention of whom, measured how, by when, at what cost? A workable approach turns the fog into structure. Define a concrete target (renewals in the first ninety days). Gather the information that matters most (why recent customers left). Generate several plausible moves rather than one. Then test the cheapest reversible one and watch the result. You have not found the single right answer; you have built a good-enough path and left room to adjust.

Contrast that with balancing a chequebook or solving a jigsaw. The goal is exact, the information is all present, and there is one correct result you can verify. These well-defined problems reward careful execution of known rules, not reframing or judgement. Applying the messy-problem toolkit here — endless stakeholder consultation, reframing the goal — would only waste effort. Matching the strategy to the problem type is the whole point.

The distinction is well established in cognitive science. Walter Reitman, in his 1964 work on problem-solving, drew attention to problems with poorly specified goals and starting conditions. Herbert Simon developed the idea in "The Structure of Ill-Structured Problems," published in the journal Artificial Intelligence in 1973, arguing that ill-structured problems are not a separate species but ones where much of the problem information must be supplied by the solver, often retrieved piece by piece as work proceeds.

Later, the instructional researcher David Jonassen synthesised this literature — notably in a 1997 paper on well-structured and ill-structured problem-solving — stressing that most everyday and professional problems are ill-structured and that teaching should reflect it. The takeaway is consistent and widely cited: real problems are usually messy, and the first move is often to impose enough structure to begin.

• Every problem has one right answer. Ill-structured problems admit several defensible solutions, judged better-or-worse.
• You should wait until you have all the information. For open problems, complete information rarely arrives; you act on enough.
• A vague goal means you cannot start. Converting the fuzzy goal into concrete sub-goals is the start.
• The two problem types need the same approach. Tidy puzzles reward rule-following; messy problems reward reframing and judgement.

Take a problem you are currently stuck on. Ask which of the three gaps is largest: is the goal unclear, is information missing, or is there no agreed test for a good answer? Write one sentence that closes that specific gap — a sharper goal, the one fact you most need, or the criterion you will judge by. Notice how naming the gap makes the next move obvious.

Think Like a Maester: When a problem feels overwhelming, ask whether the goal, the information, or the answer test is what is actually missing.

1. What three features define a well-defined problem?
2. Name two ways an ill-structured problem can be "missing" something.
3. What did Simon mean by saying part of solving is converting a fuzzy problem into better-defined parts?
4. What is satisficing, and why does it suit open problems?
5. Why is it a mistake to apply the messy-problem toolkit to a jigsaw puzzle?

Most real problems are ill-structured: their goals are unclear, their information is incomplete, and they have no single verifiable answer — unlike the well-defined puzzles we practise in school. Cognitive scientists from Reitman to Simon to Jonassen have shown that the first task with a messy problem is to impose enough structure to work on it: sharpen the goal, gather the information that matters most, and satisfice on a good-enough solution while taking small, reversible steps. Matching your strategy to the type of problem — rule-following for tidy puzzles, reframing and judgement for messy ones — is what keeps you from solving the wrong problem well.

• Wicked Problems and Complexity
• Becoming a Master Problem-Solver