Category: Mathematical problems

Hansen's problem
Hansen's problem is a problem in planar surveying, named after the astronomer Peter Andreas Hansen (1795–1874), who worked on the geodetic survey of Denmark. There are two known points A and B, and tw
Behrens–Fisher problem
In statistics, the Behrens–Fisher problem, named after Walter Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two
Network simplex algorithm
In mathematical optimization, the network simplex algorithm is a graph theoretic specialization of the simplex algorithm. The algorithm is usually formulated in terms of a minimum-cost flow problem. T
Hurwitz problem
In mathematics, the Hurwitz problem (named after Adolf Hurwitz) is the problem of finding multiplicative relations between quadratic forms which generalise those known to exist between sums of squares
Erdős discrepancy problem
No description available.
Yamabe problem
The Yamabe problem refers to a conjecture in the mathematical field of differential geometry, which was resolved in the 1980s. It is a statement about the scalar curvature of Riemannian manifolds: Let
Clock angle problem
Clock angle problems are a type of mathematical problem which involve finding the angle between the hands of an analog clock.
Birthday problem
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox is that, counterintuitively, t
Hadwiger–Nelson problem
In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson, asks for the minimum number of colors required to color the plane such that no two points at distan
Vertex enumeration problem
In mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the ob
Prescribed scalar curvature problem
In Riemannian geometry, a branch of mathematics, the prescribed scalar curvature problem is as follows: given a closed, smooth manifold M and a smooth, real-valued function ƒ on M, construct a Riemann
Dissection problem
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this
Finite volume method for three-dimensional diffusion problem
Finite volume method (FVM) is a numerical method. FVM in computational fluid dynamics is used to solve the partial differential equation which arises from the physical conservation law by using discre
Postage stamp problem
The postage stamp problem is a mathematical riddle that asks what is the smallest postage value which cannot be placed on an envelope, if the latter can hold only a limited number of stamps, and these
Dirichlet problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on
Parity problem (sieve theory)
In number theory, the parity problem refers to a limitation in sieve theory that prevents sieves from giving good estimates in many kinds of prime-counting problems. The problem was identified and nam
Circulation problem
The circulation problem and its variants are a generalisation of network flow problems, with the added constraint of a lower bound on edge flows, and with flow conservation also being required for the
Plateau's problem
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who
Littlewood–Offord problem
In mathematical field of combinatorial geometry, the Littlewood–Offord problem is the problem of determining the number of of a set of vectors that fall in a given convex set. More formally, if V is a
Riemann–Hilbert problem
In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential equations in the complex plane. Several existe
Finite lattice representation problem
In mathematics, the finite lattice representation problem, or finite congruence lattice problem, asks whether every finite lattice is isomorphic to the congruence lattice of some finite algebra.
Invariant subspace problem
In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded operator on a complex Banach space sends some no
Whitehead problem
In group theory, a branch of abstract algebra, the Whitehead problem is the following question: Is every abelian group A with Ext1(A, Z) = 0 a free abelian group? Saharon Shelah proved that Whitehead'
The monkey and the coconuts
The monkey and the coconuts is a mathematical puzzle in the field of Diophantine analysis that originated in a magazine fictional short story involving five sailors and a monkey on a desert island who
Klee's measure problem
In computational geometry, Klee's measure problem is the problem of determining how efficiently the measure of a union of (multidimensional) rectangular ranges can be computed. Here, a d-dimensional r
Josephus problem
In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. A number of people are standing in a circle waiting
Block-stacking problem
In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire, also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks
Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to
Waring's problem
In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers raised to the power k.
Snellius–Pothenot problem
The Snellius–Pothenot problem is a problem in planar surveying. Given three known points A, B and C, an observer at an unknown point P observes that the segment AC subtends an angle and the segment CB
Squaring the square
Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous a
Regiomontanus' angle maximization problem
In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem posed by the 15th-century German mathematician Johannes Müller (also known as Regiomontanus). The probl
Cheryl's Birthday
"Cheryl's Birthday" is a logic puzzle, specifically a knowledge puzzle. The objective is to determine the birthday of a girl named Cheryl using a handful of clues given to her friends Albert and Berna
Social golfer problem
In discrete mathematics, the social golfer problem (SGP) is a combinatorial-design problem derived from a question posted in the usenet newsgroup sci.op-research in May 1998. The problem is as follows
Moment problem
In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequences of moments More generally, one may consider for an arbitrary sequence of f
Rope-burning puzzle
In recreational mathematics, rope-burning puzzles are a class of mathematical puzzle in which one is given lengths of rope, fuse cord, or shoelace that each burn for a given amount of time, and matche
Boolean Pythagorean triples problem
The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of all red or all blue me
Tarski's circle-squaring problem
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equ
Spherical Bernstein's problem
The spherical Bernstein's problem is a possible generalization of the original Bernstein's problem in the field of global differential geometry, first proposed by Shiing-Shen Chern in 1969, and then l
Hausdorff moment problem
In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence (m0, m1, m2, ...) be the sequence of moments of some Borel
Znám's problem
In number theory, Znám's problem asks which sets of k integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znám's proble
Schoenflies problem
In mathematics, the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan curves in the plane it is often refe
Prescribed Ricci curvature problem
In Riemannian geometry, a branch of mathematics, the prescribed Ricci curvature problem is as follows: given a smooth manifold M and a symmetric 2-tensor h, construct a metric on M whose Ricci curvatu
Mountain climbing problem
In mathematics, the mountain climbing problem is a problem of finding the conditions that two functions forming profiles of a two-dimensional mountain must satisfy, so that two climbers can start on t
Stable marriage problem
In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of element
Mrs. Miniver's problem
Mrs. Miniver's problem is a geometry problem about the area of circles. It asks how to place two circles and of given radii in such a way that the lens formed by intersecting their two interiors has e
Oberwolfach problem
The Oberwolfach problem is an unsolved problem in mathematics that may be formulated either as a problem of scheduling seating assignments for diners,or more abstractly as a problem in graph theory, o
Monty Hall problem
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The p
Stable roommates problem
In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching f
Carpenter's rule problem
The carpenter's rule problem is a discrete geometry problem, which can be stated in the following manner: Can a simple planar polygon be moved continuously to a position where all its vertices are in
Lattice problem
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central to the constructi
Hamburger moment problem
In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m0, m1, m2, ...), does there exist a positive Borel measure μ (for instance
Zarankiewicz problem
The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgr
Zero-sum problem
In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group G and a positive integer n, one
Alhazen's problem
Alhazen's problem, also known as Alhazen's billiard problem, is a mathematical problem in geometrical optics first formulated by Ptolemy in 150 AD.It is named for the 11th-century Arab mathematician A
Minimum-cost flow problem
The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network. A typical application of this
Mathematical problem
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the plane
Newton's minimal resistance problem
Newton's minimal resistance problem is a problem of finding a solid of revolution which experiences a minimum resistance when it moves through a homogeneous fluid with constant velocity in the directi
Cauchy problem
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem can be an in
Orchard-planting problem
In discrete geometry, the original orchard-planting problem asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane. It is also called th
Class number problem
In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields (for negative integer
Kuratowski's closure-complement problem
In point-set topology, Kuratowski's closure-complement problem asks for the largest number of distinct sets obtainable by repeatedly applying the set operations of closure and complement to a given st
Square trisection
In geometry, a square trisection is a type of dissection problem which consists of cutting a square into pieces that can be rearranged to form three identical squares.
Knight's tour
A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once. If the knight ends on a square that is one knight's move from the beginning sq
Firing squad synchronization problem
The firing squad synchronization problem is a problem in computer science and cellular automata in which the goal is to design a cellular automaton that, starting with a single active cell, eventually
Turán's brick factory problem
Unsolved problem in mathematics: Can any complete bipartite graph be drawn with fewer crossings than the number given by Zarankiewicz? (more unsolved problems in mathematics) In the mathematics of gra
Traveling tournament problem
The traveling tournament problem (TTP) is a mathematical optimization problem. The question involves scheduling a series of teams such that: 1. * Each team plays every other team twice, once at home
No-three-in-line problem
The no-three-in-line problem in discrete geometry asks how many points can be placed in the grid so that no three points lie on the same line. This number is at most , because points in a grid would i
Prouhet–Tarry–Escott problem
In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials are all equal.That is, the two multisets shou
Happy ending problem
In mathematics, the "happy ending problem" (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement: Theorem — any set of five points in t
Napkin ring problem
In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled
Water pouring puzzle
Water pouring puzzles (also called water jug problems, decanting problems, measuring puzzles, or Die Hard with a Vengeance puzzles) are a class of puzzle involving a finite collection of water jugs of
Newton–Pepys problem
The Newton–Pepys problem is a probability problem concerning the probability of throwing sixes from a certain number of dice. In 1693 Samuel Pepys and Isaac Newton corresponded over a problem posed to
Congruence lattice problem
In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilwo
Seven Bridges of Königsberg
The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topo
Basel problem
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonh
Illumination problem
Illumination problems are a class of mathematical problems that study the illumination of rooms with mirrored walls by point light sources.
Eight queens puzzle
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, co
Halting problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to ru
Napoleon's problem
Napoleon's problem is a compass construction problem. In it, a circle and its center are given. The challenge is to divide the circle into four equal arcs using only a compass. Napoleon was known to b
Kirkman's schoolgirl problem
Kirkman's schoolgirl problem is a problem in combinatorics proposed by Rev. Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states: Fifteen young
Necklace splitting problem
Necklace splitting is a picturesque name given to several related problems in combinatorics and measure theory. Its name and solutions are due to mathematicians Noga Alon and Douglas B. West. The basi
Dining cryptographers problem
In cryptography, the dining cryptographers problem studies how to perform a secure multi-party computation of the boolean-XOR function. David Chaum first proposed this problem in the early 1980s and u
Stieltjes moment problem
In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (m0, m1, m2, ...) to be of the form for some measure μ. If