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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. Every problem requires an answer or solution.
- In mathematics, a problem is a question about mathematical objects and structures requiring explanation and proof. These questions range from very specific ("What are the real solutions of x2 − 1 = 0?") to quite general ("Why do these numbers appear in apparently different situations? Formulate and prove a conjecture.")
- 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.
- In business, 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.
From Ancient Greek πρόβλημα (problema) "anything thrown forward, hindrance, obstacle, anything projecting, a headland, promontory", from προβάλλω (proballo) "to throw or lay something in front of someone, to put forward", from prefix προ- (pro-) "in front of" + βάλλω (ballo) "to throw, to cast, to hurl".
- Problem solving
- Open problem - List of unsolved problems
- How to Solve It
- Optimization problem
- Decision problem
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