Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Solving |
SolvingNoun1. Finding a solution to a problem. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "solving" was first used in popular English literature: sometime before 1415. (references) |
(From Wikipedia, the free Encyclopedia)
A two-player game can be "solved" on several levels.
- Ultra-weak: In the weakest sense, solving a game means proving whether the first player will win, lose, or draw from the initial position, given perfect play on both sides.
- Weak: More typically, solving a game means providing an algorithm which secures a win for one player, or a draw for either, against any possible moves by the opponent, from the initial position only.
- Strong: The strongest sense of solution requires an algorithm which can produce perfect play from any position, i.e. even if mistakes have already been made on one or both sides. For a game with a finite number of positions, this is always possible with a powerful enough computer, by checking all the positions. However, there is the question of finding an efficient algorithm, or an algorithm that works on computers currently available.
Solved games
- Awari (a game of the Mancala family)
- Solved by Henri Bal and John Romein at the Free University in Amsterdam, Netherlands (2002). Either player can force the game into a draw.
- Connect Four
- Solved by both Victor Allis (1988) and James Allen (1989) independently. First player can force a win.
- Gomoku
- Solved by Victor Allis (1993) First player can force a win.
- Hex
- Completely solved (definition #3) by several computers for board sizes up to 6x6.
- Jing Yang has demonstrated a winning strategy (definition #2) for board sizes 7x7, 8x8 and 9x9. [1]
- John Nash showed that all board sizes are won for the first player (definition #1).
- The discovery of an efficient general algorithm for an NxN board is unlikely as the problem has been shown to be NP-hard.
- Nim
- Completely solved for all starting configurations.
- Nine men's morris
- Solved by Ralph Gasser (1993). Either player can force the game into a draw. [1]
- Pentominoes
- Weakly solved (definition #2) by H. K. Orman. It is a win for the first player.
- Qubic
- Solved by Patashnik (1980).
- Three Men's Morris
- Trivially solvable. Either player can force the game into a draw
- Tic-tac-toe
- Trivially solvable. Either player can force the game into a draw
Partially solved games
See Also: Board game complexity
- Checkers
- Endgames up to 8 pieces have been solved. Not all early-game positions have been solved, but almost all midgame positions are solved. Contrary to popular belief, Checkers is not completely solved.
- Chess
- Completely solved (definition #3) by retrospective computer analysis for all 2- to 5-piece endgames, counting the two kings as pieces. Also solved for pawnless 3-3 and most 4-2 endgames.
- Go
- Solved (definition #3) for board sizes up to 4x4. The 5x5 board is partially solved. [1] Humans usually play on a 19x19 board (which has an enormous complexity). Therefore solving the game appears very unlikely. On the other hand, a heuristic algorithmic solution might be achievable in the future. While not mathematically complete, it could give good results in practice, perhaps beating even the best human players.
- Reversi
- solved on a 4x4 and 6x6 board as a second player win.
- mnk-games
- It is trivial to show that the second player can never win. Almost all cases have been solved weakly for k <= 4. Some results are known for k = 5. The games are drawn for k >= 8.
External link
References
- Allis, Beating the World Champion? The state-of-the-art in computer game playing. in New Approaches to Board Games Research.
- H. Jaap van den Herik, Jos W.H.M. Uiterwijk, Jack van Rijswijck, "Games solved: Now and in the future" Artificial Intelligence 134 (2002) 277–311. Online: pdf, ps
- Hilarie K. Orman: Pentominoes: A First Player Win in Games of no chance, MSRI Publications -- Volume 29, 1996, pages 339-344. Online (PDF)
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Solved board games."
Synonym: SolvingSynonym: resolution (n). (additional references) |
| Domain | Usage | |
Screenplays | Yeah, pretty much, except we drove around in a van solving mysteries (The Simpsons; writing credit: Artur Brauner; Paul Hengge) Here we are so close to solving the mystery of life and death, and they worry about their precious laws (Curse of the Faceless Man; writing credit: Jerome Bixby) | |
Source: compiled by the editor from various references; see credits. | ||
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Theater & Movies |
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High Tech |
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Source: compiled by the editor from various references; see credits. | |||
| Thumbnail | Description & Credit | Thumbnail | Description & Credit |
 | The Hubble telescope has made an important contribution toward solving one of astronomy's ... Credit: NASA. |  | International School Of Crystallography : 18th Course: Direct Methods of Solving Crystal Structures. Credit: National Library of Medicine. |
 | America for the Red Man. The most practical way of solving the Indian question / / Th. Nast. Father Winter placing obstructions on the track / Bellew. Credit: Library of Congress. | ||
Source: pictures compiled by the editor from various references; see picture credits. | |||
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| "Rubics Master" by Ryan Glanzer Commentary: "Joe Allen, ranked #44 in the world for rubics cubes, works on solving a puzzle in 20 seconds." |
Source: photographs selected by the editor, with permission from the photographers. |
| Author | Quotation |
Bill Vaughan | Everything is much simpler today -- instead of solving a problem, you just subsidize it. |
Karl Menninger | Unrest of spirit is a mark of life; one problem after another presents itself and in the solving of them we can find our greatest pleasure. |
Source: compiled by the editor from various references. | |
| Subject | Topic | Quote |
Health | Neuropsychological tests measure memory, problem solving, attention, counting, and language. (references) | |
Better understanding of those common related disorders will go a long way toward solving the problem of PSP, just as studying PSP may help shed light on Parkinson's and Alzheimer's diseases. (references) | ||
In the past year, NIA-supported investigators also have looked at ways to improve standardized tests of memory, language, and other neuropsychological components in hopes of being able to better predict future development of AD. In one study, scientists at Harvard and the Massachusetts General Hospital examined whether it was possible to identify aspects of the Clinical Dementia Rating (CDR) scale to predict which people with “questionable” AD have a high likelihood of converting to a diagnosis of AD over time (Daly et al., 2000). The CDR is a semi-structured clinical interview that stages AD from 0 (normal) to 0.5 (questionable), 1.0 (mild), 2.0 (moderate), and 3.0 (severe), based on an assessment of six categories of function (memory, orientation, judgment and problem solving, community affairs, home and hobbies, and personal care). (references) | ||
Business | Koreans hope that this operation may offer them a more innovative means of solving their dioxin emission problems. (references) | |
Economic History | Indonesia | The court system does not provide effective recourse for solving commercial disputes. (references) |
Australia | Australian industry is known for its ingenuity and practical approach to problem solving. (references) | |
Poland | Solving air, soil and water pollution problems is a major priority for the Polish government. (references) | |
Human Rights | Ghana | In 2000 the military authorities appealed to the public to desist from involving the military in solving personal disputes. (references) |
South Africa | There continued to be killings as a result of the factional and intraparty rivalry in the Nongoma area, and authorities had limited success in solving three related killings. (references) | |
Mexico | Human rights organizations and the U.N. Special Rapporteur on the Independence of Judges and Lawyers, Dato Param Cumaraswamy, who visited the country in May, strongly criticized the Government's limited progress in solving these murders. (references) | |
Political Economy | Mexico | Major judicial reforms have made some progress toward solving these systemic problems, and the current Supreme Court has recently emphasized its independence from the President, the Congress, and the political parties. (references) |
Women | Poland | In 1998 the police, in cooperation with the State Agency for Solving Alcoholic Problems, introduced the "blue card," a record-keeping system designed to better document incidents of spousal abuse. (references) |
Worker Rights | Guatemala | It also reported a significant gap between the problems regarding workers' rights and the resources applied by the Government to solving these problems. (references) |
Source: compiled by the editor from ICON Group International, Inc.; see credits. | ||
| Speaker | Term | Phrase(s) |
Calvin Coolidge | 1923-1929 | The wisest and soundest method of solving our tax problem is through economy. |
Harry S. Truman | 1945-1953 | We have a record of enormous achievements as a democratic society in solving problems and meeting opportunities as they developed. |
Lyndon B. Johnson | 1963-1969 | If ever there was a nation that was capable of solving its problems, it is this Nation. |
Gerald Ford | 1974-1977 | This Nation can be proud of significant achievements in recent years in solving problems and crises. |
Jimmy Carter | 1977-1981 | My Administration has taken great strides toward solving the difficult problems faced by older Americans. |
Source: compiled by the editor from various references. | ||
| "Solving" is generally used as a lexical verb (-ing form) -- approximately 96.85% of the time. "Solving" is used about 538 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Lexical Verb (-ing form) | 96.85% | 521 | 11,694 |
| Noun (singular) | 2.04% | 11 | 106,044 |
| Noun (proper) | 0.93% | 5 | 157,705 |
| Adjective (general or positive) | 0.19% | 1 | 339,140 |
| Total | 100.00% | 538 | N/A |
Source: compiled by the editor from several corpora; see credits.
| Country | Name |
| France | Solving International |
| (more examples...) |
Source: compiled by the editor from Icon Group International, Inc.
Expressions using "solving": Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases ♦ heuristic problem solving ♦ Polynomial System Solving ♦ problem solving ♦ radiosity solving. Additional references. | |
| Hypenated Usage | |
Ending with "solving": puzzle-solving. | |
Containing "solving": problems-for-the-solving-of. | |
| Source: compiled by the editor from various references; see credits. | |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Language | Translations for "solving"; alternative meanings/domain in parentheses. | |
Chinese | 解决 (resolved, resolving, settlement, solve, solved). (various references) | |
Danish | løsning af Golfkrisen (solving the Gulf Crisis), heuristisk problemloesning (heuristic problem solving), ESTEAM (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM), arkitektur for interaktiv problemløsing ved hjælp af samarbejdende data-og videnbaser (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM). (various references) | |
Dutch | oplossing van de Golfcrisis (solving the Gulf Crisis), heuristische probleemoplossing (heuristic problem solving), ESTEAM (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM), architectuur voor interactieve probleemoplossing door samenwerkende data-en kennisbases (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM). (various references) | |
Finnish | vuorovaikutteisen ongelmanratkaisun rakenne tieto-ja tietämyskantojen yhteistoiminnalla(ESTEAM (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM), heuristinen ongelmanratkaisu (heuristic problem solving). (various references) | |
French | dénouant. (various references) | |
German | lösend (detaching, disengaging, loosing, solvent, unfastening, unfixing). (various references) | |
Greek | Ευρετική λύση προβλήματος (heuristic problem solving). (various references) | |
Hebrew | פתירה (solution). (various references) | |
Hungarian | megoldás (accomplishment, clearing up, denouement, disentanglement, expedient, resolving, resort, solution, there is no choice, unravelling). (various references) | |
Italian | soluzione (resolution, settlement, solution). (various references) | |
Japanese Kanji | 追及 (carrying out, gaining on). (various references) | |
Japanese Katakana | ついきゅう (carrying out, close enquiry, enquiry, gaining on, investigation, pursuing). (various references) | |
Korean | 해결. (various references) | |
Pig Latin | olvingsay.(various references) | |
Portuguese | solução de problemas por heurística (heuristic problem solving), resolução de problemas por método heurístico (heuristic problem solving), resolução da crise do Golfo (solving the Gulf Crisis), ESTEAM (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM), arquitectura para a solução interactiva de problemas pela cooperação de bases de dados e conhecimento (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM). (various references) | |
Russian | решать решение. (various references) | |
Spanish | solución heurística de problemas (heuristic problem solving), resolución de problemas (solving problems), resolución de la crisi del Golfo (solving the Gulf Crisis), ESTEAM (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM), arquitectura para solución interactiva de problemas con la cooperación de bases de datos y de conocimientos (Architecture for Interactive Problem Solving by Cooperating Data and Knowledge Bases, ESTEAM). (various references) | |
Swedish | lösning (answer, key, liquor, lotion, settlement, solution, working). (various references) | |
Turkish | halletme (adjustment, removal, settlement, solution, working, working out), çözme (disengaging, undoing, untieing, working out). (various references) | |
| Source: compiled by the editor from various translation references. | ||
Derivations | |
Words ending with "solving": absolving, dissolving, redissolving, resolving. (additional references) | |
| |
"Solving" is suggested in spellcheckers for the following: olving, salvini, selfing, Selvin, Shovlin, solvint, sulfing. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "solving" (pronounced sÄ"lving) |
| 5 | -Ä" l v i ng | absolving, evolving, involving, resolving, revolving. |
| 4 | -l v i ng | delving, dissolving, shelving. |
| 3 | -v i ng | approving, achieving, arriving, behaving, believing, braving, calving, caregiving, carving, caving, conceiving, conniving, conserving, craving, curving, deceiving, depriving, deriving, deserving, disapproving, disbelieving, diving, driving, earthmoving, engraving, forgiving, giving, grieving, halving, having, heaving, improving, interleaving, interweaving, jiving, leaving, lifesaving, living, loving, misbehaving, misgiving, moving, observing, paving, perceiving, preserving, proving, raving, receiving, relieving, reliving, removing, reserving, retrieving, reviving, revving, saving, serving, shaving, shoving, sieving, skydiving, starving, staving, striving, surviving, thanksgiving, thieving, thriving, unbelieving, undeserving, unforgiving, unnerving, unswerving, waiving, waving, weaving. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "g-i-l-n-o-s-v" | |
-1 letter: losing, loving, soling, voling. | |
-2 letters: lingo, lings, linos, lions, loins, longs, noils, sling, vinos, viols. | |
-3 letters: gins, ions, ling, lino, lins, lion, logs, loin, long, nils, nogs, noil, oils, sign, silo, sing, slog, snog, soil, soli, song, vigs, vino, viol. | |
-4 letters: gin, gos, ins, ion, lin, lis, log, nil, nog, nos, oil, ons, sin. | |
| Words containing the letters "g-i-l-n-o-s-v" | |
+1 letter: salvoing. | |
+2 letters: absolving, resolving, shoveling, solvating. | |
+3 letters: convulsing, dissolving, evildoings, flavorings, lovingness, novelising, shovelling, valorising, vocalising. | |
+4 letters: laborsaving, levigations, longevities, lovemakings, observingly, oversalting, overselling, sovereignly, vainglories, vanpoolings. | |
+5 letters: bolshevizing, convalescing, griseofulvin, invigilators, lovingnesses, overindulges, oversleeping, overslipping, redissolving, slaveholding, vainglorious, volatilising. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Modern | 5. Usage: Commercial 6. Images: Photo Album 7. Images: Digital Art 8. Quotations: Familiar | 9. Quotations: Non-fiction 10. Quotations: Speeches 11. Usage Frequency 12. Names: Company Usage | 13. Expressions 14. Expressions: Internet 15. Translations: Modern 16. Derivations | 17. Rhymes 18. Anagrams 19. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
