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The main purpose of a problem statement is to identify and explain the problem. [3] [4] Another function of the problem statement is as a communication device. [3] Before the project begins, stakeholders verify the problem and goals are accurately described in the problem statement. Once approved, the project reviews it.
Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC.
Examples include finding a perfect strategy for chess positions on an N × N board [15] and similar problems for other board games. [16] The problem of deciding the truth of a statement in Presburger arithmetic requires even more time.
Sleeping Beauty problem: A probability problem that can be correctly answered as one half or one third depending on how the question is approached. Three Prisoners problem , also known as the Three Prisoners paradox: [ 3 ] A variation of the Monty Hall problem .
The problem statements and descriptions are sometimes linked between both documents. An 8D can utilize pre-brainstormed information from a FMEA to assist in looking for potential problems. Possible causes in a FMEA can immediately be used to jump start 8D Fishbone or Ishikawa diagrams .
In discussions of problem structuring methods, it is common to distinguish between two different types of situations that could be considered to be problems. [17] Rittel and Webber's distinction between tame problems and wicked problems (Rittel & Webber 1973) is a well known example of such types. [17]
For example, the decision problem "is the input even?" is formalized as the set of even numbers. A decision problem whose input consists of strings or more complex values is formalized as the set of numbers that, via a specific Gödel numbering, correspond to inputs that satisfy the decision problem's criteria.
The problem to determine all positive integers such that the concatenation of and in base uses at most distinct characters for and fixed [citation needed] and many other problems in the coding theory are also the unsolved problems in mathematics.