Find plain-language definitions, practical examples, and related methods for the logic, investigation, decision, and puzzle-design terms used on problem.so.
Use each definition to distinguish ideas that are often confused, then follow its method link when you need a worked process.
These terms describe how clues restrict possible answers and how a solver proves that an answer works.
A candidate is one answer, value, placement, or explanation that has not yet been ruled out. Good solving keeps candidates visible until a clue or test removes them.
Example: In a matching puzzle, each unmarked person and time pairing remains a candidate.
See the repeatable logic-solving method for a worked process.
A constraint is a rule that limits which combinations are allowed. Hard constraints must be satisfied. Preferences should be recorded separately so an inconvenient option is not mistaken for an impossible one.
Example: A meeting room that holds eight people cannot host a group of twelve.
See the constraint satisfaction guide for a worked process.
The contrapositive is a logically equivalent way to reverse and negate a conditional statement. If P implies Q, then not Q implies not P. The converse, Q implies P, is not automatically valid.
Example: If approval produces a reference number, no reference number means the request was not approved under that rule.
See the conditional logic guide for a worked process.
A deduction is a conclusion that must follow from the stated facts and rules. It is stronger than a guess because every competing candidate that contradicts the same evidence can be removed.
Example: If only one time remains legal for Ada, assigning Ada to that time is a deduction.
See the logic and deductive reasoning hub for a worked process.
Uniqueness means exactly one answer satisfies all stated rules. Finding one working answer proves that an answer exists, but it does not prove that every alternative fails.
Example: Swapping two unresolved assignments is a quick test for a second valid solution.
See the fair puzzle design guide for a worked process.
Verification checks a proposed answer against every requirement, clue, or predicted result. It is a separate step from producing the answer and should be possible for another reader to repeat.
Example: A finished grid is verified by retesting each clue and checking for an alternate arrangement.
See the logic mistake checklist for a worked process.
These terms help separate observations, explanations, choices, and tests in real-world problem solving.
An assumption is a belief that a plan or explanation depends on but that is not yet supported strongly enough for the decision. Important assumptions should be written down and tested.
Example: A new form will reduce support calls assumes customers can find and complete it.
See the assumption mapping guide for a worked process.
A bottleneck is the step that currently limits the output of the whole process. Improving a non-bottleneck may make that step faster without improving total completion time.
Example: If review can approve ten cases per day, faster intake alone cannot raise daily completed cases above ten.
See the bottleneck analysis guide for a worked process.
A hard constraint is a requirement that a feasible answer cannot violate. Options that fail one should be removed before preferences are scored or compared.
Example: A supplier that lacks a required safety certification is infeasible regardless of its price score.
See the decision matrix guide for a worked process.
A hypothesis is a proposed explanation that predicts evidence. A useful test asks what would look different if that explanation were true instead of a competing explanation.
Example: If retries cause the delay, disabling retries in a controlled test should reduce queue growth.
See the hypothesis-driven problem-solving guide for a worked process.
A problem statement defines the observable gap between the current and expected condition, including the affected group, boundary, measure, and time. It should not assume a cause or prescribe a solution.
Example: Mobile checkout completion fell from the expected range during the last release window.
See the problem statement guide for a worked process.
A root cause is a changeable mechanism supported by evidence that helps explain why an unwanted event occurred or escaped detection. A person, correlation, or early timeline event is not enough by itself.
Example: Missing input validation can be a mechanism when reproducing it creates the same failure and adding it prevents recurrence.
See the root cause analysis guide for a worked process.
Sensitivity analysis changes uncertain inputs within reasonable ranges to see whether a conclusion remains stable. A result that changes after a small input adjustment needs more evidence before commitment.
Example: Change the largest decision weight and check whether another option becomes the winner.
See the weighted decision matrix calculator for a worked process.
A soft constraint is a preference or cost that may be traded against another preference. It affects which feasible answer is better, but violating it does not make the answer impossible.
Example: A shorter commute may be preferred even though a longer commute remains feasible.
See the constraint satisfaction guide for a worked process.
No. A symptom is an observed effect. A useful problem statement describes the measurable gap and boundary without claiming that the first visible symptom is the cause. The problem statement method keeps these parts separate.
An assumption is something a plan depends on. A hypothesis is a proposed explanation that makes a testable prediction. An assumption can be rewritten as a hypothesis when you define what evidence should change your confidence.
Stop when the evidence is sufficient for the next safe, reversible action and you have defined a signal that would reopen the analysis. High-risk or irreversible decisions require a stronger stopping rule than low-cost experiments.
Retest every clue, enumerate the remaining candidates, and try swaps or alternate branches. One working answer proves existence. A uniqueness check shows that no second candidate satisfies the same rules.
