Chapter Summary Chapter 17, "Examinations and other puzzles," challenges the reader to look beyond the surface of a problem to identify its creator and their intent. The authors argue that many difficulties, particularly in academic and testing environments, are artificial constructs where the context of the problem—specifically who wrote it and why—provides the most critical clues for the solution,. Using examples ranging from PhD comprehensive exams to programmer aptitude tests, the text illustrates how analyzing the structure of the answers or the biases of the tester can reveal the solution without requiring the actual work the problem ostensibly demands,. The chapter distinguishes between "problems" and "puzzles," noting that puzzles are difficult by design, leading solvers to ignore obvious solutions in favor of complex ones,. Ultimately, the chapter posits that asking "Who sent this problem?" allows the solver to outwit the designer, whether that designer is a trickster professor or a military adversary,.
The Contextual Crutch of Education The chapter begins by satirizing the educational system, noting that while most schoolchildren know where babies come from, they seem to believe exam problems are delivered by storks. This metaphor highlights a critical failure in how problem-solving is taught. In a typical classroom setting, students do not need to identify the nature of a problem because the context is provided for them. If the class has been studying "Light and Optics" for the past week, the homework problems will inevitably require the application of optics formulas, not the Laws of Thermodynamics.
The authors point out that students become dependent on this external context. They learn to solve problems by association rather than definition. This system works until the "fatal instant" of the final examination. During a final exam, the temporal context is removed; a problem could be derived from any of the fifteen weeks of instruction. Stripped of the clue "what did we study this week?", students are often crushed because they have lost the one variable they relied upon most: the source of the problem.
Analyzing the Progenitor: "Who Sent This?" The text argues that the "real world" complaints students make about school are often misplaced; school fails to prepare them even for the "world of final examinations" because it hides the human origin of problems. To survive high-stakes testing, the authors suggest the clever student must "read" the exam to identify its specific author.
The chapter uses the example of PhD comprehensive examinations. Despite the name, these exams are rarely comprehensive; rather, they reflect the narrow interests of specific faculty members. The first step in solving such a problem is deduction:
By asking "Where does the problem come from?", the solver moves beyond the raw data of the question and addresses the psychological requirements of the person who will be grading the answer.
The Mechanics of Aptitude Tests The authors provide a tactical breakdown of how to dismantle multiple-choice "aptitude" tests by analyzing the designer's intent rather than the content of the questions. They assert that standardized tests are constructed objects, not natural phenomena, and they follow specific design rules.
For example, a problem on a timed exam cannot require a method that takes longer than the allotted time. If a solver's approach is too time-consuming, it is intrinsically the wrong approach for that specific format, regardless of its mathematical elegance.
The text details a specific example from a "programmer aptitude test" involving arithmetic skills. The authors claim such questions can often be answered without doing any arithmetic at all. They present a sample set of answers: (a) 31938 (b) 31929 (c) 31928 (d) 32928 (e) 31828
The logic provided is that the test designer wants to catch students who are "off by a little bit". Therefore, the wrong answers are usually derivations of the right answer, incorporating common calculation errors (like being off by one digit). By studying the structure of the answers, one can see that choice (c) 31928 is the "center" of the variance. Choice (b) is off by one digit in the ones column; choice (d) is off by one digit in the thousands column; choice (e) is off by one digit in the hundreds column. Because (c) is the reference point for the "distractor" answers, it must be the correct solution.
In this scenario, the question itself becomes a "time-wasting distraction." The solver sidesteps the arithmetic entirely by asking the governing question of the chapter: "Who sent this problem? What's he trying to do to me?".
Puzzles vs. Problems The chapter draws a sharp distinction between a "problem" and a "puzzle."
This distinction is crucial because it changes the solver's psychology. The authors use the "chess problem" to illustrate this. In the world of chess puzzles, the solution is never an "obvious" move (like putting the king in check immediately) because that would make the puzzle too easy. A person immersed in puzzle-solving will automatically filter out simple solutions, assuming the problem must be "cooked" (constructed to be tricky).
This creates a vulnerability. If a puzzle-solver encounters a problem that is simple, but they believe it to be a puzzle, they will overlook the solution. The authors note that a solver becomes angry when a puzzle turns out to be solved by an obvious move, feeling they have been tricked by the lack of complexity.
Military Implications: The "Plain Text" Trap The chapter concludes by applying this concept to military communications, contrasting the artificial difficulty of puzzles with the pragmatic difficulty of conflict.
Because the intercepting cryptanalysts know the source is an enemy (a "designer" of problems), they cannot accept the message at face value. They waste time looking for the hidden pattern or the trick, unable to believe the solution is staring them in the face. The authors suggest that real-world problems (even military ones) are often simpler than puzzles because real adversaries have limitations and characteristics that reduce the number of possibilities, whereas puzzle designers operate in a world of artificial complexity.
Conclusion Chapter 17 reinforces the book's central theme that the definition of the problem depends heavily on the source of the problem. Whether facing a professor, a test-maker, or an enemy general, the most effective solver is the one who looks past the "question" to understand the motivations and methods of the "questioner".