A problem is the relation between human will and reality. When will and reality do not coincide, the resolution of this gap between reality and will is the solution of the problem. A problem implies a desired outcome coupled with an apparent deficiency, doubt or inconsistency that prevents the outcome from taking place.
- Mathematical problem is a question about mathematical objects and structures that may require a distinct answer or explanation or proof. Examples include mathematical exercises and word problems at school level or deep theorems 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, regarding the Gospels' relationship to each other.
- 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 rocks that forces the climber to climb.
- In reading, a problem is a combination of a series of words with the overall plotline, which the reader must attempt to decipher.
- In walking, a mobility problem is presented. Motion is achieved via mechanical interaction of the legs and a surface.
- Problems Problem brainstorming site with tools to solve them.