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.

Etymology

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".

Problem Solving

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. Many problems have no discovered solution and are therefore classified as an open problem.

From the mid 20th century, the field of theoretical computer science has explored the use of computers to solve problems.

Examples

• 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.
• 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. A good example of this type of problem is the travelling salesperson problem which is based on calculating the most efficient route between many places
• In computability theory a decision problem requires a simple yes-or-no answer.
• In rock climbing a problem is a series of climbing holds that forces the climber to plan and execute a certain maneuver.