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This is a list of puzzles that cannot be solved. An impossible puzzle is a puzzle that cannot be resolved, either due to lack of sufficient information, or any number of logical impossibilities. 15 Puzzle – Slide fifteen numbered tiles into numerical order. It is impossible to solve in half of the starting positions. [1]
Another definition is "a problem whose social complexity means that it has no determinable stopping point". [3] Moreover, because of complex interdependencies, the effort to solve one aspect of a wicked problem may reveal or create other problems. Due to their complexity, wicked problems are often characterized by organized irresponsibility.
Determining if a context-free grammar generates all possible strings, or if it is ambiguous. Given two context-free grammars, determining whether they generate the same set of strings, or whether one generates a subset of the strings generated by the other, or whether there is any string at all that both generate.
The Kissing Number Problem. A broad category of problems in math are called the Sphere Packing Problems. They range from pure math to practical applications, generally putting math terminology to ...
NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory.
Characterise word-representable near-triangulations containing the complete graph K 4 (such a characterisation is known for K 4-free planar graphs [130]) Classify graphs with representation number 3, that is, graphs that can be represented using 3 copies of each letter, but cannot be represented using 2 copies of each letter [131]
When used in this way, the stronger notion (such as "strong antichain") is a technical term with a precisely defined meaning; the nature of the extra conditions cannot be derived from the definition of the weaker notion (such as "antichain"). sufficiently large, suitably small, sufficiently close
One of the widely used types of impossibility proof is proof by contradiction.In this type of proof, it is shown that if a proposition, such as a solution to a particular class of equations, is assumed to hold, then via deduction two mutually contradictory things can be shown to hold, such as a number being both even and odd or both negative and positive.