A **problem** is an obstacle, impediment, difficulty or challenge, or any situation that invites resolution; the resolution of which is recognized as a solution or contribution toward a known purpose or goal. A problem implies a desired outcome coupled with an apparent deficiency, doubt or inconsistency that prevents the outcome from taking place.

### Other articles related to "problem, problems":

... A divide and conquer algorithm works by recursively breaking down a

**problem**into two or more sub-

**problems**of the same (or related) type, until these become simple enough to be solved directly ... The solutions to the sub-

**problems**are then combined to give a solution to the original

**problem**... of efficient algorithms for all kinds of

**problems**, such as sorting (e.g ...

**Problem**

... The necklace

**problem**is a

**problem**in recreational mathematics, solved in the early 21st century ...

**Problem**

... field of graph theory the Hamiltonian path

**problem**and the Hamiltonian cycle

**problem**are

**problems**of determining whether a Hamiltonian path or a Hamiltonian cycle exists in a given graph (whether ... Both

**problems**are NP-complete ...

**Problem**- Background

... Y2K is a numeronym and was the common abbreviation for the year 2000 software

**problem**... (rather than literal) roll-over of the millennium, even though the

**problem**could have occurred at the end of any ordinary century ... The Year 2000

**problem**was the subject of the early book, Computers in Crisis by Jerome and Marilyn Murray (Petrocelli, 1984 reissued by McGraw-Hill under the title The Year 2000 Computing ...

... To solve this

**problem**, it suffices to provide an upper bound on the total degree of the such a bound reduces the

**problem**to a finite system of linear equations that may be solved by usual linear algebra ... A related

**problem**is the ideal membership

**problem**, which consists in testing if a polynomial belongs to an ideal ... For this

**problem**also, a solution is provided by a upper bound on the degree of the A general solution of the ideal membership

**problem**provides an effective Nullstellensatz, at least for the weak form ...

### Famous quotes containing the word problem:

“From cradle to grave this *problem* of running order through chaos, direction through space, discipline through freedom, unity through multiplicity, has always been, and must always be, the task of education, as it is the moral of religion, philosophy, science, art, politics and economy; but a boy’s will is his life, and he dies when it is broken, as the colt dies in harness, taking a new nature in becoming tame.”

—Henry Brooks Adams (1838–1918)

“It is commonplace that a *problem* stated is well on its way to solution, for statement of the nature of a *problem* signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.”

—John Dewey (1859–1952)

“Theology, I am persuaded, derives its initial impulse from a religious wavering; for there is quite as much, or more, that is mysterious and calculated to awaken scientific curiosity in the intercourse with God, and it [is] a *problem* quite analogous to that of theology.”

—Charles Sanders Peirce (1839–1914)