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Structured problem improvement approach
A3 problem solving is a structured problem-solving and continuous-improvement approach, first employed at Toyota and typically used by lean manufacturing
A3_problem_solving
Process of achieving a goal by overcoming obstacles
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from
Problem_solving
Topics referred to by the same term
C/2023 A3 (Tsuchinshan–ATLAS) , a comet also called A3 A3 problem solving, a structured problem solving and continuous improvement approach, first employed
A3
Method of identifying the fundamental causes of faults or problems
A3 problem solving – Structured problem improvement approach Eight disciplines problem solving – Eight disciplines of team-oriented problem solving method
Root-cause_analysis
Problem-solving tools
lit. 'theory of inventive problem solving') is a methodology which combines an organized, systematic method of problem-solving with analysis and forecasting
TRIZ
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Iterative interrogative technique
Fantin, Ivan (2014). Applied Problem Solving. Method, Applications, Root Causes, Countermeasures, Poka-Yoke and A3. Ivan Fantin. ISBN 978-1499122282
Five_whys
Measures of product quality
constant level Eight disciplines problem solving – Eight disciplines of team-oriented problem solving method A3 problem solving Garvin, David A. (1987). "Competing
Eight_dimensions_of_quality
Decision problem in computer science
ISBN 0-7167-1045-5. A3.2: SP13, pg.223. Lagarias, J. C.; Odlyzko, A. M. (1985-01-01). "Solving low-density subset sum problems". Journal of the ACM.
Subset_sum_problem
Problem optimization method
sub-problems means that the space of sub-problems must be small, that is, any recursive algorithm solving the problem should solve the same sub-problems over
Dynamic_programming
a_{1}a_{2}a_{3}\ldots \ } where a0 is an integer, the integer part of x, and a1, a2, a3, ... are integers between 0 and 9. Given this representation the number x
Hermite's_problem
Decision problem pertaining to equivalence of expressions
problems are undecidable, i.e. there is no general algorithm for solving this problem. This even holds if we limit the systems to have finite presentations
Word_problem_(mathematics)
Problems which attempt to find the most efficient way to pack objects into containers
asymptotically O(a3/5). Packing squares in a circle: Good solutions are known for n ≤ 35. Packing identical rectangles in a rectangle: The problem of packing
Packing_problems
Geometry problem about finding touching circles
circles be denoted as C1, C2 and C3. Van Roomen solved the general problem by solving a simpler problem, that of finding the circles that are tangent to
Problem_of_Apollonius
Type of mathematical expression
equation. Solving Diophantine equations is generally a very hard task. It has been proved that there cannot be any general algorithm for solving them, or
Polynomial
Humorous chess puzzle
Novotny, and Lacny), joke chess problems are enjoyed for some twist. In some cases the composer plays a trick to prevent a solver from succeeding with typical
Joke_chess_problem
Problem in computer science
A3.1: SP3, pg.221. Vazirani, Vijay V. (2001). Approximation Algorithms. Springer-Verlag. ISBN 978-3-540-65367-7. [1]: A Pascal program for solving the
Set_packing
Form of reasoning
rhetoric Case-based reasoning – Process of solving new problems based on the solutions of similar past problems Correlation does not imply causation – Refutation
Deductive_reasoning
Polynomial-time algorithm for the assignment problem
Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods
Hungarian_algorithm
Controlled-access highway in Italy
The Autostrada A3 is an autostrada (Italian for "motorway") 53.6 kilometres (33.3 mi) long in Italy located in the region of Campania, which runs from
Autostrada_A3_(Italy)
Recreational mathematics planar boundary and area problem
problem is either of two related problems in recreational mathematics involving a tethered goat grazing a circular area: the interior grazing problem
Goat_grazing_problem
3rd-century Greek mathematician
Diophantine equations. The methods for solving such equations is called Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. Diophantus
Diophantus
Polynomial equation of degree 3
Hippocrates, Menaechmus and Archimedes are believed to have come close to solving the problem of doubling the cube using intersecting conic sections, though historians
Cubic_equation
Chess opening
Nc6 6.Ngf3 Be7 7.0-0 0-0 8.e5 Nd7 9.Re1 b5 10.Nf1 b4 11.h4 a5 12.Bf4 a4 13.a3 bxa3 14.bxa3 Na5 15.Ne3 Ba6 16.Bh3 d4 17.Nf1 Nb6 18.Ng5 Nd5 19.Bd2 Bxg5 20
King's_Indian_Attack
Strongly NP-complete problem in computer science
The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned
3-partition_problem
Polynomial function of degree 4
F_{1}(x)\times F_{2}(x)=x^{4}+cx^{2}+dx+e.} We therefore can solve the quartic by solving for s and then solving for the roots of the two factors using the quadratic
Quartic_function
Abstract strategy board game
8×8 board with a computer search, solving all the possible openings. In 2013, Jakub Pawlewicz and Ryan B. Hayward solved all openings for 9×9 boards, and
Hex_(board_game)
Computer that uses photons or light waves
Hamiltonian path problem. The simplest problem is the subset sum problem. An optical device solving an instance with four numbers {a1, a2, a3, a4} is depicted
Optical_computing
Expression of symbolic information
to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations
Formula
Chess opening
E24 – 4.a3 (E24–E29 cover the Sämisch Variation) E25 – 4.a3 Bxc3+ 5.bxc3 c5 E26 – 4.a3 Bxc3+ 5.bxc3 c5 6.e3 E27 – 4.a3 Bxc3+ 5.bxc3 0-0 E28 – 4.a3 Bxc3+
Nimzo-Indian_Defence
Nazi ballistic missile series
area. As part of Operation Lighthouse the first A3 was launched on 4 December 1937, but suffered problems with premature parachute deployment and engine
Aggregat
Thought experiment on artificial intelligence
981. Searle 2009, p. 1. Simon, H., & Newell, A. (1958). Heuristic Problem Solving: The Next Advance Operations Research, 6(1), 1-10 Quoted in Crevier
Chinese_room
years. Attempts have been made to solve the problem pointed out by Pryce, known as Pryce's theorem, and other problems with the composite photon theory
Neutrino_theory_of_light
Australian and American mathematician (born 1975)
arXiv:2012.04125. doi:10.4310/ACTA.2022.v229.n2.a3. Bloom, Thomas (15 June 2026). "Erdős Problems". Erdős Problems. Retrieved 16 July 2026. "Vitae". UCLA. Retrieved
Terence_Tao
American children's television show
for the problem-solving portions of an episode, as did their comprehension and problem solving. Anderson stated, "As children learned how to solve the problems
Blue's_Clues
Chess variant played on a 6×6 board without bishops
ISBN 0-9524142-0-1. Newell, Allen; Simon, Herbert Alexander (2019). Human problem solving. Brattleboro, Vermont: Echo Point Books & Media. ISBN 978-1-63561-792-4
Los_Alamos_chess
Method of exponentiation using a minimal number of multiplications
addition chain for a15 above, the subproblem for a6 must be computed as (a3)2, since a3 is re-used (as opposed to, say, a6 = a2(a2)2, which also requires three
Addition-chain_exponentiation
Networking protocol for clock synchronization
packet, t 3 + θ − δ / 2 = t 2 {\displaystyle t_{3}+\theta -\delta /2=t_{2}} Solving for θ yields the definition of the time offset. The values for θ and δ
Network_Time_Protocol
Artificial helium-like atom with a harmonic instead of Coulomb potential
force a2 = 0 and a3 = 0 respectively, and as a consequence of the three term recession, all higher coefficients also vanish. Solving for k {\displaystyle
Hooke's_atom
Graph without triples of adjacent vertices
triangle detection can be solved in time O ( m 1.407 ) {\displaystyle O(m^{1.407})} . Another approach is to find the trace of A3, where A is the adjacency
Triangle-free_graph
17th-century conjecture proved by Andrew Wiles in 1994
centuries and was solved with mathematics Fermat would not have known. The claim eventually became one of the most notable unsolved problems of mathematics
Fermat's_Last_Theorem
Chess opening
and World Chess Championship 1985. Another option after 11...Bf8 is 12.a3. With a3, White controls the b4-square further, preventing Nc6–Nb4 ideas, and
Ruy_Lopez,_Zaitsev_Variation
Geometric technique for designing mechanical linkages
center point for A is the center of the circle that passes through A1, A2 and A3 in the three positions. Similarly, the center point for B is the center of
Burmester's_theory
Unproved conjecture in mathematics
curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
educational measurement refers to a "simplified description of human problem solving on standardized educational tasks, which helps to characterize the
Attribute_hierarchy_method
Problem-solving technique in applied mathematics using order-of-magnitude approximations
equilibrium equation: Scale analysis is very useful and widely used tool for solving problems in the area of heat transfer and fluid mechanics, pressure-driven wall
Scale_analysis_(mathematics)
Chess test suite
Bc2 Kf3 a3 bxa3 Bxa3 g6 Bxg6 Bxb3 Kf8 Ke2 Bf5 f3 Bd7 Bc4 Bc1 Kf2 Ba4 FEN r1b2rk1/1p1nbppp/pq1p4/3B4/P2NP3/2N1p3/1PP3PP/R2Q1R1K w - - 0 15 Problem 10 Van
Nolot
Chess opening
.Bb7 5.a3 became the more common move order to reach the Petrosian system by the mid-1980s, where White has avoided 4.a3 c5 5.d5 Ba6 and 4.a3 Ba6. 5.Bg5
Queen's_Indian_Defense
Appendix on analytic geometry by Descartes
the distances to the other two lines (in the four line case). In solving these problems and their generalizations, Descartes takes two line segments as
La_Géométrie
Theorem in geometry
including the first of the published solutions. Indeed, the Woodburn Problem Solving Group, as it might be known today, was sufficiently well known by then
Napoleon's_theorem
Cubic polynomials defined from a monic polynomial of degree four
cubic is defined only when P(x) is a quartic in depressed form—that is, when a3 = 0. Note that the fourth and fifth definitions below also make sense and
Resolvent_cubic
1974 book by Robert M. Pirsig
usually able to diagnose and repair himself through the use of rational problem-solving skills. For example, when the narrator and his friends come into Miles
Zen and the Art of Motorcycle Maintenance
Zen_and_the_Art_of_Motorcycle_Maintenance
Underground railway cars
electricity. A3 trains have begun refurbishment for A3-64 and A3-66 from 2003 to 2006, known as A3E, but 8 trains were scrapped in 2000. Based on the A3, the
Berlin_U-Bahn_rolling_stock
Root-finding algorithm
= 9.26891, so we set a3 = a2 and b3 = −1.42897. In the fourth iteration, we use inverse quadratic interpolation between (a3, f(a3)) = (−4, −25) and (b2
Brent's_method
Chess opening
abandon protection of the d5-knight with 9.a3, a move Yakov Estrin recommended, but Black is quite strong after 9.a3 Nxc2+ 10.Kd1 Nd4!? or 10...Nxa1! 11.Nxd5
Fried_Liver_Attack
Properties underlying modern physics
powerful methods for solving problems and predicting what can happen. While conservation laws do not always give the answer to the problem directly, they form
Symmetry_in_quantum_mechanics
Alternate storytelling in media
lessons of ARGs to similarly take advantage of new media and collective problem–solving". As such, implementation of ARGs in these different settings involves
Alternate_reality_game
Type of prime number
1978 that if all the factors of p − 1 are less than logc p, then the problem of solving discrete logarithm modulo p is in P. Therefore, for cryptosystems
Strong_prime
Hungarian mathematician
open problems. In 2016, Pyber and Endre Szabó proved that in a finite simple group L of Lie type, a generating set A of L either grows, i.e., |A3| ≥ |A|1+ε
László_Pyber
German battle rifle
mount. The Ak 4D will be used by the Swedish Army as a stop-gap DMR. DIO G3-A3 Bullpup: Iranian bullpup variant of the G3. The Pakistani models are manufactured
Heckler_&_Koch_G3
Chess opening
dxe4 5.a3, followed by either 5...Be7 6.Nxe4, returning the pawn, or 5...Bxc3+ 6.Nxc3 Nc6, holding on to the pawn. 4.Bd3, defending e4. 4.a3 Bxc3+ 5
French_Defence
Chess opening
queen's knight does little to utilize White's advantage of the first move. On a3, the knight does not control central squares, and White would have to move
Durkin_Opening
Mathematical relation making a non-equal comparison
Inequalities (Lecture notes). Shapiro, Harold (2005). "Mathematical Problem Solving". The Old Problem Seminar. Kungliga Tekniska högskolan. "3rd USAMO". Archived
Inequality_(mathematics)
Object-oriented software design pattern
subcategorized as a creational pattern. The factory method design pattern solves problems such as: How can an object's subclasses redefine its subsequent and
Factory_method_pattern
Chinese automobile manufacturer
Chuanfu, Chairman and President of BYD Company, released "Xuanji A3" (Chinese: 璇玑A3), BYD's 567th automobile-grade chip and first in-house developed assisted
BYD_Auto
Graph structure studied in group theory
a, a2, a3} in the multiplication table, with a4 = e. The inverse a−1 = a3 is also a generator of this cycle: (a3)2 = a2, (a3)3 = a, and (a3)4 = e. Similarly
Cycle_graph_(algebra)
Technique to compress data
L} is the maximum length of a codeword. No algorithm is known to solve this problem in O ( n ) {\displaystyle O(n)} or O ( n log n ) {\displaystyle
Huffman_coding
Chess opening
Black to trade the b4-bishop with 11.Nb3 followed by 12.a3, Black has the reply 11...a4 12.a3 Bc3! keeping the balance. The move ...Bb4+ can also be effective
Budapest_Gambit
Use of a GPU for computations typically assigned to CPUs
algorithm solving the resource-constrained project scheduling problem is freely available on GitHub; the GPU algorithm solving the nurse scheduling problem is
General-purpose computing on graphics processing units
General-purpose_computing_on_graphics_processing_units
American activist (born 1973)
Tonight with John Oliver, where they discussed the importance of solving the problem of public shaming and how her situation may have been different if
Monica_Lewinsky
Details of data storage in a spreadsheet application
552} A 2 := 27.399 {\displaystyle A2:=27.399} A 3 := 26.246 {\displaystyle A3:=26.246} and the following cells contain the following formulas B 1 := A 1
Numeric precision in Microsoft Excel
Numeric_precision_in_Microsoft_Excel
United States historic place
2005). "Time Capsule of Hawaiian King Located". The Victoria Advocate. p. A3. "Radar quickly pinpoints site of Kamehameha V capsule". Honolulu Star-Bulletin
Aliʻiōlani_Hale
Propaganda term for WWII German weapons programmes
term Wunderwaffe now generally refers to a universal solution which solves all problems related to a particular issue, mostly used ironically for its illusionary
Wunderwaffe
Submarine-launched ballistic missile
missiles and cover a range up to fifteen hundred miles. A problem that needed to be solved was that this design would not be able to carry the desired
UGM-27_Polaris
Polynomial equation of degree 4
F_{1}F_{2}=x^{4}+cx^{2}+dx+e\qquad \qquad (4)} We therefore can solve the quartic by solving for w and then solving for the roots of the two factors using the quadratic
Quartic_equation
British mathematician (1916–2020)
mathematician Paul Erdős. Erdős was noted for posing and solving difficult mathematical problems and shared several of them with Guy. Guy later recalled
Richard_K._Guy
American CIA analyst and Soviet spy (1941–2026)
"Money wasn't only reason Ames sold U.S. secrets". Waterloo Courier. p. A3. Retrieved January 3, 2014 – via Newspaperarchive.com.{{cite news}}: CS1 maint:
Aldrich_Ames
Conjecture in number theory
Beal conjecture is the following conjecture in number theory: Unsolved problem in mathematics If A x + B y = C z {\displaystyle A^{x}+B^{y}=C^{z}} where
Beal_conjecture
Chess opening
seek counterplay on the kingside. 7...a6 Black forces White's knight back to a3. 8.Na3 The immediate 8.Bxf6 forces 8...gxf6, when after 9.Na3, Black can transpose
Sicilian Defence, Sveshnikov Variation
Sicilian_Defence,_Sveshnikov_Variation
American talk radio host (1934–2022)
records and began chatting with callers. He got the reputation of being a problem-solver, and comedian Mort Sahl, a big fan of his, jokingly called him "the
Michael Jackson (radio commentator)
Michael_Jackson_(radio_commentator)
Kingdom is similarly inaccessible from the rest of the United Kingdom. The A3 (UK) and N54 (Ireland) road, known as the Concession Road, crosses the border
List_of_enclaves_and_exclaves
American serial rapist and serial killer (born 1945)
California and has been called second only to Virginia's in effectiveness in solving cold cases. In an attempt to increase awareness, crime writer Michelle
Joseph_James_DeAngelo
Italian ocean liner that sank in 1956
on her maiden voyage on 14 December 1952, but amid reports of machinery problems during sea trials, the departure was delayed to 14 January 1953. Following
SS_Andrea_Doria
South Korean footballer (born 1981)
Feyenoord, he was scammed in his country, and took a two-week vacation to solve the problem. He had difficulty concentrating on football due to his case of fraud
Lee_Chun-soo
American cryptographer (born 1947)
partial words in documents; he later published this work as a journal paper.[A3] His research from this time on self-organizing lists[A4] became one of the
Ron_Rivest
Simple polynomial map exhibiting chaotic behavior
intermittent chaos. If the parameter is considered to be a decreasing from a3, this is a type of emergence of chaos. As the parameter moves away from the
Logistic_map
Angers Critics of the Military". The New York Times. Reuters. 1989-10-09. p. A3. Retrieved 2021-06-24. "Strange case of kidnapping". The Independent. April
List of solved missing person cases (1970s)
List_of_solved_missing_person_cases_(1970s)
Chess opening
Qc2 Bb7 10.Bd2 Ra7 11.Rc1 Be4 12.Qb3 Nc6 13.e3 Qa8 14.Qd1 Nb8 15.Ba5 Rc8 16.a3 Bd6 17.Nbd2 Bd5 18.Qf1 Nbd7 19.b4 e5 20.dxe5 Bxe5 21.Nxe5 Nxe5 22.f3 Nc4 23
Catalan_Opening
Chess opening
problem glossary joke chess Chess prodigy Elo rating system Mechanical Turk Simultaneous exhibition Tie-breaking in Swiss-system tournaments Solving chess
English_Opening
Argument for the existence of God
be God." The argument from contingency is formulated as the Third Way (Q2, A3) in the Summa Theologica. It may be expressed as follows: There exist contingent
Cosmological_argument
Branch of logic
example, for m = 3 we must find an A3 and B3 such that the duplicator always wins the 3-move game. This can be achieved by A3 = {1, ..., 8} and B3 = {1, ..
Finite_model_theory
Chinese automobile manufacturing company
outside the Anhui province for several years. During that period, Chery solved the problem by piggybacking on a SAIC Motor license until 2003. In this period
Chery
Chess opening
problem glossary joke chess Chess prodigy Elo rating system Mechanical Turk Simultaneous exhibition Tie-breaking in Swiss-system tournaments Solving chess
Zukertort_Opening
Advantage of White over Black in chess
Dorfman, Ron (28 October 2007). "The 'Bilbao Draw' – how it doesn't solve the problem". chessbase.com. ChessBase. Retrieved 21 January 2024. Friedel, Frederic
First-move_advantage_in_chess
Physics formula
R with the screen. The integration is performed over the areas A1, A2 and A3, giving U ( P ) = 1 4 π [ ∫ A 1 + ∫ A 2 + ∫ A 3 ] ( U ∂ ∂ n ( e i k s s )
Kirchhoff's diffraction formula
Kirchhoff's_diffraction_formula
South Korean self-propelled 155 mm howitzer
cavitation. Using the recommended TK-6-03-01012 antifreeze did not solve the problem, suggesting that the antifreeze was not the cause of the issue. A
K9_Thunder
Chess opening
problem glossary joke chess Chess prodigy Elo rating system Mechanical Turk Simultaneous exhibition Tie-breaking in Swiss-system tournaments Solving chess
Barnes_Opening
Professional ice hockey league season
Depression was starting to take its toll on the NHL. In attempts to solve financial problems, the Pittsburgh Pirates moved to Philadelphia and became the Philadelphia
1930–31_NHL_season
pieces, see Fairy chess piece; terms specific to chess problems, see Glossary of chess problems; terms specific to computer chess, see Glossary of computer
Glossary_of_chess
Function with unusual fractal properties
rationals, by means of the identification of a1, a2, a3, … with the continued fraction [0; a1, a2, a3,…]. Since both S : x ↦ x x + 1 {\displaystyle S:x\mapsto
Minkowski's question-mark function
Minkowski's_question-mark_function
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING
A3 PROBLEM-SOLVING