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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. Kookrooster maken 23; 15 Puzzle – Slide fifteen numbered tiles into numerical order. It is impossible to solve in half of the starting positions. [1]
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.
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine [ edit ]
For example, x²-6 is a polynomial with integer coefficients, since 1 and -6 are integers. The roots of x²-6=0 are x=√6 and x=-√6, so that means √6 and -√6 are algebraic numbers.
For example, 11 can be 2-split into 2+9, 3+8, 4+7, and 5+6. The respective products are 18, 24, 28, and 30 and the players put a tick mark beside each of these products in their tables (Table 1). When they are done, some numbers have no tick marks, some have one, and some have more than one. Sue now looks at her sum and all its 2-splits.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Can 3SUM be solved in strongly sub-quadratic time, that is, in time O(n 2−ϵ) for some ϵ>0? Can the edit distance between two strings of length n be computed in strongly sub-quadratic time? (This is only possible if the strong exponential time hypothesis is false.) Can X + Y sorting be done in o(n 2 log n) time?
This is a list of some of the major unsolved problems, puzzles, or questions in economics. Some of these are theoretical in origin and some of them concern the inability of orthodox economic theory to explain an empirical observation.