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Mathematical puzzle of avoiding crossings
The three utilities problem, also known as water, gas and electricity, is a mathematical puzzle that asks for non-crossing connections to be drawn between
Three_utilities_problem
a time. Three utilities problem – Connect three cottages to gas, water, and electricity without crossing lines. Thirty-six officers problem – Arrange
List_of_impossible_puzzles
Non-orientable surface with one edge
the utility graph, a six-vertex complete bipartite graph whose embedding into the Möbius strip shows that, unlike in the plane, the three utilities problem
Möbius_strip
Branch of the mathematical field of graph theory
edges intersecting. A basic embedding problem often presented as a mathematical puzzle is the three utilities problem. Other applications can be found in
Topological_graph_theory
Classic problem in graph theory
graph theory Hamiltonian path Icosian game Travelling salesman problem Three utilities problem Euler, Leonhard (1741). "Solutio problematis ad geometriam
Seven_Bridges_of_Königsberg
On minimizing crossings in bicliques
much older puzzle, the three utilities problem, can be seen as a special case of the brick factory problem with three kilns and three storage facilities.)
Turán's_brick_factory_problem
Topics referred to by the same term
and three wells", the Three utilities problem Two Wells This disambiguation page lists articles associated with the title Three Wells. If an internal
Three_Wells_(disambiguation)
Problem of allocation of money by consumers in order to most benefit themselves
In microeconomic theory, the utility maximization problem formalizes how a consumer allocates limited resources across different goods and services. The
Utility_maximization_problem
Problem or enigma that tests a person's ingenuity
Königsberg, the three cups problem, and three utilities problem Sangaku (Japanese temple tablets with geometry puzzles) A chess problem is a puzzle that
Puzzle
Graph that can be embedded in the plane
to certain constraints is constructed as part of the game play Three utilities problem, a popular puzzle Trudeau, Richard J. (1993), Introduction to Graph
Planar_graph
Concept in economics and decision theory
bundles, ordinal utilities are only the rankings of utilities received from different bundles of goods or services. For example, ordinal utility could tell
Utility
Fewest edge crossings in drawing of a graph
planar graph formed by replacing each crossing by a new vertex Three utilities problem, the puzzle that asks whether K3,3 can be drawn with 0 crossings
Crossing number (graph theory)
Crossing_number_(graph_theory)
Geometry problem on grid points
Unsolved problem in mathematics How many points can be placed in an n-by-n grid so that no three of them lie on a line? More unsolved problems in mathematics
No-three-in-line_problem
Computer utility software
computer. The latest version of the original series of Norton Utilities is Norton Utilities 16 for Windows XP/Vista/7/8, released 26 October 2012. Peter
Norton_Utilities
Concept in economics
expected utility, not the numerical values of those expected utilities. The class of constant relative risk aversion utility functions contains three categories
Expected_utility_hypothesis
Puzzle in logic and mathematics
The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for
Two_envelopes_problem
Post used by public utilities to support overhead wires and related equipment
few utilities. These nails are considered valuable to collectors, with older dates being more valuable, and unique markings such as the utilities' name
Utility_pole
Process of identifying and labeling public utility mains that are underground
of the presence of underground utilities. For various reasons, including security, the precise location of the utilities may not be indicated. The only
Utility_location
1979 nuclear accident in Pennsylvania
were even less pleased with the utility (General Public Utilities) and the plant designer. According to the IAEA, the Three Mile Island accident was a significant
Three_Mile_Island_accident
Benefit derived from consuming a product
based upon the respective marginal utilities of the goods that they have or desire (with these marginal utilities being distinct for each potential trader)
Marginal_utility
In contrast with ordinal utility, in economics
ordinal utilities imply cardinal utilities. This result is now known as the von Neumann–Morgenstern utility theorem; many similar utility representation
Cardinal_utility
Any individual whose preferences satisfy four axioms has a utility function
(whereas continuity is used to set aside lexicographic or infinitesimal utilities). Completeness assumes that an individual has well defined preferences:
Von Neumann–Morgenstern utility theorem
Von_Neumann–Morgenstern_utility_theorem
Designate Financial Market Utilities as Systemically Important" (PDF). Federal Register. 75 (244). "Financial Market Utilities: Is the System Safer?" (PDF)
Systemically important financial market utility
Systemically_important_financial_market_utility
Computer bugs related to the year 2000
The Year 2000 problem (Y2K) was the potential for computer errors on the Gregorian calendar related to the formatting and storage of calendar data for
Year_2000_problem
Algorithmic problem on pairs of sequences
within the original sequences. The problem of computing longest common subsequences is a classic computer science problem. Because it is polynomial and has
Longest_common_subsequence
American Energy Corporation
In 1999, Con Edison and Northeast Utilities entered negotiations that would have created one of the largest utilities in the United States. However, Con
Eversource_Energy
Concept in economics
Cobb–Douglas is a special case of the CES utility, with ρ → 0 {\displaystyle \rho \rightarrow 0\,} .) The marginal utilities are given by U 1 ( x , y ) = α ( α
Indifference_curve
Paradox involving a game with repeated coin flipping
ergodicity problem was made by Peters in 2011. These solutions are mathematically similar to using the Kelly criterion or logarithmic utility. General dynamics
St._Petersburg_paradox
Preference ranking
economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it
Ordinal_utility
Pareto efficiency implies utilitarian rule
{\displaystyle W} can be represented as a linear combination of individual utilities: W ( x ) = ∑ i = 1 n a i u i ( x ) + c {\displaystyle W(x)=\sum
Harsanyi's utilitarian theorem
Harsanyi's_utilitarian_theorem
Ethical theory based on maximizing well-being
monetary values, wealth maximization can reconcile the problem of interpersonally adding "utilities". Critics counter that wealthier parties can effectively
Utilitarianism
Conflict of interest when one person acts on another's behalf
The principal–agent problem (often abbreviated agency problem) refers to the conflict in interests and priorities that arises when one person or entity
Principal–agent_problem
Type of boat designed for transporting amphibious forces and cargo to shore
A landing craft utility (LCU) is a type of boat used by amphibious forces to transport equipment and troops to the shore. They are capable of transporting
Landing_craft_utility
Problem in continuous-time finance
between stocks and a risk-free asset so as to maximize expected utility. The problem was formulated and solved by Robert C. Merton in 1969 both for finite
Merton's_portfolio_problem
Intelligence in machines
typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in
Artificial_intelligence
Dam in Yiling District, Hubei, China
The Three Gorges Dam, officially known as Yangtze River Three Gorges Water Conservancy Project is a hydroelectric gravity dam that spans the Yangtze River
Three_Gorges_Dam
distribution 3,2,0,0, where the utilities are 3,3,2,2,3. The Nash product rule finds a budget-allocation maximizing the product of utilities. It is Pareto efficient
Donor_coordination
Problem in ethics
The mere addition paradox (also known as the repugnant conclusion) is a problem in population ethics identified by Derek Parfit and discussed in his book
Mere_addition_paradox
Function in decision theory
agent has additive-independent utilities, he must be indifferent between these two lotteries. A fundamental result in utility theory is that, two attributes
Multi-attribute_utility
Game theory solution
agreement between the players. The coordinates of an agreement are the utilities of the players if this agreement is implemented. The assumption that F
Kalai–Smorodinsky bargaining solution
Kalai–Smorodinsky_bargaining_solution
YouTube channel
work has been received positively by critics, with Line Goes Up – The Problem with NFTs as a noted work. Scholar Christina Wurst labeled Folding Ideas
Folding_Ideas
Philosophical question
The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: "Should the properties
Problem_of_universals
Conformance of AI to intended objectives
with the alignment problem, the principal and the agent differ in their utility functions. But in contrast to the alignment problem, the principal cannot
AI_alignment
Information theorem
that there is an equivalence between three possible rankings of information structures: one based in expected utility, one based in informativeness, and
Blackwell's informativeness theorem
Blackwell's_informativeness_theorem
This is a list of some of the major problems in philosophy. A statement is a conditional statement with a false antecedent. For example, the statement
List of philosophical problems
List_of_philosophical_problems
Fair division problem
agents with cardinal utilities. It means that no agent prefers the lottery of another agent. CEEI is ex-ante EF w.r.t. expected utilities. Necessary EF (or
Fair_random_assignment
Rawlsian decision rule for social choice
satisfies the following three properties: Pareto efficiency; Pigou-Dalton principle; Independence of common utility pace - if all utilities are transformed by
Egalitarian_rule
Support programs included in or available for IBM OS/360 and successors
Facilities (DSF) IDC Access Method Services (AMS) IEB Dataset utilities. Dataset utilities "are used to reorganize, change, or compare data at the data
Support programs for OS/360 and successors
Support_programs_for_OS/360_and_successors
American energy company
service in the borough of Manhattan; Orange and Rockland Utilities, Inc., a regulated utility serving customers in a 1,300-square-mile (3,400 km2) area
Consolidated_Edison
Sequence of characters that forms a search pattern
regular language. They came into common use with Unix text-processing utilities. Different syntaxes for writing regular expressions have existed since
Regular_expression
Prime Minister of the United Kingdom since 2026
rewired Britain". Burnham set out three "clear tasks" for Number 10 North; to increase public ownership of essential utilities such as water, energy and housing
Andy_Burnham
Means by which a person dies by suicide
person with serious physical injuries, long-term health problems, or brain damage. Worldwide, three suicide methods predominate, with the pattern varying
Suicide_methods
is a discontinued utility software suite by Symantec Corp. It integrates three of Symantec's most popular products – Norton Utilities, Norton CrashGuard
Norton_SystemWorks
The Health Utilities Index (HUI) is a rating scale used to measure general health status and health-related quality of life (HRQoL). HUI questionnaires
Health_Utilities_Index
Game in algorithmic game theory
games as a computational problem, is given by Papadimitriou & Roughgarden 2008). Graphical games are games in which the utilities of each player depends
Succinct_game
Mathematical concept
multi-objective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives. For a multi-objective
Multi-objective_optimization
Range of SUVs manufactured by the Ford Motor Company
Brand Sales up 17 Percent for the Year in U.S.; Fuel-Efficient Cars, Utilities, Trucks Drive Sales Gains" (PDF). media.ford.com (Press release). January
Ford_Explorer
Stone, bronze and iron ages of pre-history
1910, the Swedish archaeologist, Knut Stjerna, addressed another problem of the Three-Age System: although a culture was predominantly classified as one
Three-age_system
Financial phenomenon
identified by economist Jeremy Siegel in 1972. Like the related two envelopes problem, the phenomenon is sometimes labeled a paradox because an agent can seem
Siegel's_paradox
Discontinued American military vehicle
The M151, or officially: Truck, Utility, ¼-Ton, 4×4, was the successor to the Korean War M38 and M38A1 Jeep Light Utility Vehicles. Despite being a clean-sheet
M151_¼-ton_4×4_utility_truck
power-log utilities and negative-exponential utilities, the predictions do not depend on canceling subjective probabilities. A second problem is that some
Utility_assessment
Presumed Russian secret radio station
The Squeaky Wheel Distinctive two-tone and three-tone channel markers for the Squeaky Wheel Problems playing this file? See media help. The Squeaky Wheel
The_Squeaky_Wheel
Bicycling as transportation
Utility cycling encompasses any cycling done simply as a means of transport rather than as a sport or leisure activity. It is the original and most common
Utility_cycling
Fair item allocation problem
with dichotomous utilities and even with additive utilities. ( Σ 2 P {\displaystyle \Sigma _{2}^{\textrm {P}}} is the class of problems that can be solved
Envy-free_item_allocation
American utility company
two smaller utilities, Midland Counties Public Service and the Fresno Water Company, which was later sold. The acquisition of these utilities did not result
Pacific Gas and Electric Company
Pacific_Gas_and_Electric_Company
System utility in Microsoft Windows
that run during startup process to help the user determine the cause of a problem with Windows. Some of its functionality varies by Windows versions: In
MSConfig
Field of machine learning
Formulating the problem as a Markov decision process assumes the agent directly observes the current environmental state; in this case, the problem is said to
Reinforcement_learning
Shell command for comparing file content
are included in the diffutils package with other diff and patch related utilities. Postprocessors sdiff and diffmk render side-by-side diff listings and
Diff
Ability to attribute mental states to oneself and others
tests on autistic people may be misinterpreted based on the double empathy problem, which proposes that rather than autistic people specifically having trouble
Theory_of_mind
Concept in United States patent law
inventions in the future.[citation needed] In a pharmaceutical context, the utility problem usually arises when there is a patent claim on a new drug, but the
Utility (patentability requirement)
Utility_(patentability_requirement)
American electric utility
services. Its ten electric utility operating companies comprise one of the United States' largest investor-owned utilities, based on serving six million
FirstEnergy
Management of the flow of resources
provide garbage collection, mail deliveries, public utilities, and after-sales services, logistical problems must be addressed. Logistics deals with the movement
Logistics
Text string used to uniquely identify a computer file
unspecified binary data, etc.) The components required to identify a file by utilities and applications varies across operating systems, as does the syntax and
Filename
Type of social dilemma
theory, expected utility theory). Game theory assumes that individuals are rational actors motivated to maximize their utilities. Utility is often narrowly
Collective_action_problem
Government agency in charge of water supply
The Public Utilities Board, abbreviated as PUB, is a statutory board under the Ministry of Sustainability and the Environment of the Government of Singapore
Public_Utilities_Board
Decision that leads to the best outcome in decision theory
the expected utility (a probability–weighted average of utility over all possible outcomes of a decision). Sometimes, the equivalent problem of minimizing
Optimal_decision
Situation where total gains match total losses
independent of the opponent's strategy. This leads to a linear programming problem with the optimal strategies for each player. This minimax method can compute
Zero-sum_game
Preliminary phase of architectural and urban design processes
these circulation gateways. Information for utilities concerning the site can be found through the utility departments and companies in the local area
Site_analysis
Pricing problem in Marxism
20th-century discussions of Karl Marx's economics, the transformation problem is the problem of finding a general rule by which to transform the "values" of
Transformation_problem
File format and file archiver program
pax C.4 Utilities in The Open Group Base Specifications Issue 6, 2004 Edition, opengroup.org – indicates tar as removed pax – Shell and Utilities Reference
Tar_(computing)
Hitch for attaching implements to tractors
expensive Farmall F-30 model. The hitch's utility and simplicity have since made it an industry standard. The three-point hitch is a system of components
Three-point_hitch
Distributed data processing framework
Apache Hadoop (/həˈduːp/) is a collection of open-source software utilities for reliable, scalable, distributed computing. It provides a software framework
Apache_Hadoop
American woman acquitted of murder (1860–1927)
Street and Belmont Street, several office buildings, shares in several utilities, two cars and a large amount of jewelry. She left $30,000 (equivalent
Lizzie_Borden
American rape victim (1961–1986)
victim and exposes the victim to a variety of social and psychological problems." There was national debate about the issue of releasing the victim's name
Cheryl_Araujo
Problem optimization method
social welfare function. In Ramsey's problem, this function relates amounts of consumption to levels of utility. Loosely speaking, the planner faces the
Dynamic_programming
In mains electricity, part of a circuit connected to ground or earth
protected against overcurrent on the neutral conductor. Common grounding problems and concerns can include the following: A ground connection that is missing
Ground_and_neutral
Natural number
numbers (as a lower limit). Unsolved problem in mathematics Is 5 the only odd, untouchable number? More unsolved problems in mathematics In graph theory, all
5
Ability to make choices voluntarily
"Intricately related to the hard problem of consciousness, the hard problem of free will represents the core problem of conscious free will: Does conscious
Free_will
American theoretical physicist (1918–1988)
new address." Unable to focus on research problems, Feynman began tackling physics problems, not for utility, but for self-satisfaction. One of these involved
Richard_Feynman
German steel and weapons production company
world wars. It produced battleships, U-boats, tanks, howitzers, guns, utilities, and hundreds of other commodities. The company also produced steel used
Krupp
Value that a party would ideally get
bargaining is the abstract problem of selecting a feasible vector of utilities, as a function of the set of feasible utility vectors (fair division is
Entitlement_(fair_division)
Economic issue of securities
In finance, a holdout problem occurs when a bond issuer is in default or nears default, and launches an exchange offer in an attempt to restructure debt
Holdout_problem
Process to choose a course of action
published under the label problem solving, particularly in European psychological research. Decision-making can be regarded as a problem-solving activity yielding
Decision-making
American politician (born 1953)
million in campaign donations from oil and gas companies and electric utilities over the course of his political career. In 2018, he joined the Climate
Fred_Upton
Elliptic partial differential equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation
Poisson's_equation
Mission pack for Grand Theft Auto
London 1969" other than cosmetic changes and that "all of the gameplay problems [from the base game] remain". He criticised the lack of development citing
Grand_Theft_Auto:_London_1969
Final stage of electricity delivery to individual consumers in a power grid
and closing switches to isolate a certain section from the grid. Some utilities have smart switches (also known as trip savers) that automatically reconfigure
Electric_power_distribution
Concept in mathematical optimization
this problem had been stated in an unpublished master's thesis by William Karush in 1939. Consider the following nonlinear optimization problem in standard
Karush–Kuhn–Tucker_conditions
Former publicly traded S&P 500 electric and natural gas utility holding company
Byllesby Co., which provided engineering and management services to electric utilities. Byllesby acquired the Stillwater Gas & Electric Co. of Stillwater, Minnesota
Northern_States_Power_Company
comprises over one hundred members. This includes thirty three Utility Members that are electric utilities, Seven Independent Power Providers and over fifty
Caribbean Electric Utility Services Corporation
Caribbean_Electric_Utility_Services_Corporation
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