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A problem is an obstacle which makes it difficult to achieve a desired goal, objective or purpose. It refers to a situation, condition, or issue that is yet unresolved. In a broad sense, a problem exists when an individual becomes aware of a significant difference between what actually is and what is desired.

From Ancient Greek πρόβλημα (próblēma) "anything thrown forward, hindrance, obstacle, anything projecting, a headland, promontory", from προβάλλω (probállō) "to throw or lay something in front of someone, to put forward", from prefix προ- (pro-) "in front of" + βάλλω (bállo) "to throw, to cast, to hurl".

Every problem asks for an answer or solution. Trying to find a solution to a problem is known as problem solving. The time it takes to solve a problem is a way of measuring complexity.^[1] Many problems have no discovered solution and are therefore classified as an open problem.

See also: List of unsolved problems

• Mathematical problem is a question about mathematical objects and structures that may require a distinct answer or explanation or proof. Examples include word problems at school level or deeper problems such as shading a map with only four colours.
• In society, a problem can refer to particular social issues, which if solved would yield social benefits, such as increased harmony or productivity, and conversely diminished hostility and disruption.

See also: Wicked problem

• In business and engineering, a problem is a difference between actual conditions and those that are required or desired. Often, the causes of a problem are not known, in which case root cause analysis is employed to find the causes and identify corrective actions.
• In chess, a problem is a puzzle set by somebody using chess pieces on a chess board, for others to get instruction or intellectual satisfaction from determining the solution.
• In theology, there is what is referred to as the Synoptic Problem, which includes in its discourse a concern for assumptions of historical accuracy that are challenged by apparent contradictions in the Gospels' accounts of allegedly historical events.
• In academic discourse a problem is a challenge to an assumption, an apparent conflict that requires synthesis and reconciliation. It is a normal part of systematic thinking, the address of which adds to or detracts from the veracity of a conclusion or idea.
• An optimization problem is finding the best solution from all feasible solutions.
• In computability theory a decision problem requires a simple yes-or-no answer.

• Concern
• Heuristic
• How to Solve It
• Question
• Problem-based learning
• Problematization