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Page 557 of Mathematics Teacher Vol. 44, Issue 8 [page]

1951 Mathematics Teacher  
Additive and Multiplicative Magic Squares. Miscellanea 16.' showed how magic squares could be used in a new version of the old game of Tick-Tack-Toe.  ...  At the end of the explanation of this game was the statement, “The connection with magic squares is also obvious and might well motivate a report or project dealing with this latter topic.’’  ... 

NOISE EFFECTS IN QUANTUM MAGIC SQUARES GAME

PIOTR GAWRON, JAROSŁAW MISZCZAK, JAN SŁADKOWSKI
2008 International Journal of Quantum Information  
In the article we analyse how noisiness of quantum channels can influence the magic squares quantum pseudo-telepathy game.  ...  Therefore the game deserves more careful study aiming at its implementation.  ...  Acknowledgments This research was supported in part by the Polish Ministry of Science and Higher Education project No N519 012 31/1957.  ... 
doi:10.1142/s0219749908003931 fatcat:ezp6dpxydrfrxckyezxi2lisbu

Extending and Characterizing Quantum Magic Games [article]

Alex Arkhipov
2012 arXiv   pre-print
The Mermin-Peres magic square game is a cooperative two-player nonlocal game in which shared quantum entanglement allows the players to win with certainty, while players limited to classical operations  ...  We characterize exactly which of these games exhibit quantum pseudo-telepathy, and give quantum winning strategies for those that do.  ...  In our use, it gives a short and simple proof that a given Mermin-game is nonmagic.  ... 
arXiv:1209.3819v1 fatcat:fhipjdv4ona4xly5ch54pcfi6a

Parallel DIQKD from parallel repetition [article]

Thomas Vidick
2017 arXiv   pre-print
Our proof combines existing results on immunization (Kempe et al., SICOMP 2011) and parallel repetition (Bavarian et al., STOC 2017) of entangled games.  ...  We give an arguably simpler and more direct proof of a recent result by Miller, Jain and Shi, who proved device-independent security of a protocol for quantum key distribution in which the devices can  ...  Let MS be the two-player Magic Square game, C * MS > 0 the constant defined in (2), and γ, ε > 0 such that ε < C * MS /2.  ... 
arXiv:1703.08508v1 fatcat:q5wii35pwvgatk4trqiq7glylq

Comparing different levels of interaction constraints for deriving visual problem isomorphs

Wenwen Dou, Caroline Ziemkiewicz, Lane Harrison, Dong Hyun Jeong, Roxanne Ryan, William Ribarsky, Xiaoyu Wang, Remco Chang
2010 2010 IEEE Symposium on Visual Analytics Science and Technology  
To test our hypothesis, we conducted a user study in which participants were given different levels of interaction constraints when solving a simple math game called Number Scrabble.  ...  Number Scrabble is known to have an optimal visual problem isomorph, and the goal of this study is to learn if and how the participants could derive the isomorph and to analyze the strategies that the  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Department of Homeland Security.  ... 
doi:10.1109/vast.2010.5653599 dblp:conf/ieeevast/DouZHJRRWC10 fatcat:6edtd3wnjvhtjfeypsfbyencnu

Toward a deeper understanding of the relationship between interaction constraints and visual isomorphs

Wenwen Dou, Caroline Ziemkiewicz, Lane Harrison, Dong Hyun Jeong, William Ribarsky, Xiaoyu Wang, Remco Chang
2012 Information Visualization  
To test our hypothesis, we conducted a user study in which participants were given different levels of interaction constraints when solving a simple mathematic game called number scrabble.  ...  Number scrabble is known to have an optimal visual problem isomorph, and the goal of this study is to learn if and how the participants could derive the isomorph and to analyze the strategies that the  ...  It is clear that by transforming the number scrabble game into a magic square, this relatively difficult game of finding and adding multiple numbers becomes as simple as playing a game of tic-tac-toe.  ... 
doi:10.1177/1473871611433712 fatcat:adqipci2gzhtzlujth64eozjqi

Page 22 of Recreation Vol. 51, Issue 7 [page]

1958 Recreation  
Parties—Plans and Pro- grams. 72 pp. .70 597. Parties for Special Days of the Year. 58 pp. te 598. Parties—Musical Mixers and Simple Square Dances 51 pp. 50 PARTIES PLUS SERIES. Eth- el Bowers, Ed.  ...  MORE FUN WITH MAGIC. Joseph Leeming. Simple, -to-follow § di- rections aa diagrams for magic stunts make _ this book entertaining for all the family. 89 pp. 2.95 589. OMNIBUS OF FUN.  ... 

Page 397 of Mathematics Teacher Vol. 49, Issue 5 [page]

1956 Mathematics Teacher  
the ‘Magic Square”’ puzzle.  ...  In one of these the problem is to form a ‘““Magic Square’ by inserting into the spaces the digits 1 to 9 so that the sum in each row, column, and diagonal is exactly 15.  ... 

Winning strategies for pseudo-telepathy games using single non-local box [article]

Samir Kunkri, Guruprasad Kar, Sibasish Ghosh, Anirban Roy
2006 arXiv   pre-print
It is also shown that the magic square pseudo-telepathy game of any size can be won by using just two ebits of entanglement -- for quantum strategy, and by a single NL-box -- for non-local strategy.  ...  Using a single NL-box, a winning strategy is given for the impossible colouring pseudo-telepathy game for the set of vectors having Kochen-Specker property in four dimension.  ...  And in both of these cases they can successfully win the magic square game.  ... 
arXiv:quant-ph/0602064v2 fatcat:qprdgw3bd5gsderbwkfm7h445a

Rigidity of the magic pentagram game [article]

Amir Kalev, Carl A. Miller
2017 arXiv   pre-print
In this paper we prove ridigity for the magic pentagram game, a simple binary constraint satisfaction game involving two players, five clauses and ten variables.  ...  This property can be traced back as far as 1998 (Mayers and Yao) and has been proved for multiple classes of games.  ...  [18] to our attention, and Matthew McKague for helpful technical discussions about our proofs. AK is funded by the US Department of Defense.  ... 
arXiv:1705.06649v2 fatcat:34l3f2jpqrdh3cj2wudenhkljy

Mathematical ideas in non-western cultures

Marcia Ascher
1984 Historia Mathematica  
Games of Chance: Simple probability, expected value, fair game; tree diagrams and successive trials; early dice; fore- runners of dice and divination; the native American game of dish; a native  ...  the writings of Muhammad ibn Muhammad; De la Lotire's generating technique; using the dihedral group of squares to generate others; associated Chinese beliefs; the magic cube and magic circle  ... 
doi:10.1016/0315-0860(84)90006-5 fatcat:rnusraunbffqlkqvy3m5xj25ea

Robust self-testing for linear constraint system games [article]

Andrea Coladangelo, Jalex Stark
2019 arXiv   pre-print
We give a new proof that certain LCS games (the Mermin--Peres Magic Square and Magic Pentagram over binary alphabets, together with parallel repetitions of these) have unique winning strategies, where  ...  We equip the n-qubit Pauli group for n≥ 2 with such a presentation; our machinery produces the Magic Square and Pentagram games from the presentation and provides robust self-testing bounds.  ...  We thank Richard Cleve and Joel Wallman for sharing with the authors a proof that the magic square game mod d for d = 2 is not a pseudotelepathy game.  ... 
arXiv:1709.09267v2 fatcat:7q3llw65krgypd73foxf36kbni

Page 11 of The Cornell Engineer Vol. 9, Issue 6 [page]

1944 The Cornell Engineer  
and invented some very “magicalmagic squares.  ...  4 9 2 3 5 7 8 1 6 There is a very simple rule for making magic squares of an odd number of rows of any size that you desire. Briefly, this is it: 1.  ... 

Rigidity of the magic pentagram game

Amir Kalev, Carl A Miller
2017 Quantum Science and Technology  
In this paper we prove ridigity for the magic pentagram game, a simple binary constraint satisfaction game involving two players, five clauses and ten variables.  ...  This property can be traced back as far as 1998 (Mayers and Yao) and has been proved for multiple classes of games.  ...  square game and the magic pentagram game.  ... 
doi:10.1088/2058-9565/aa931d pmid:29431180 pmcid:PMC5803839 fatcat:vgm6gctnkvekzhz6mumdyfldb4

Mathematical Miscellanea: Odd and even—a game

P. H. Nygaard, Adrian Struyk
1956 Mathematics Teacher  
In one of these the problem is to form a "Magic Square" by inserting into the spaces the digits 1 to 9 so that the sum in each row, column, and diagonal is exactly 15.  ...  There are two well-known mathematical recreations that start with a square framework consisting of three rows and three columns, each with three cells.  ...  the ‘Magic Square”’ puzzle.  ... 
doi:10.5951/mt.49.5.0397 fatcat:ertufr2fpfdyllbjllmf3fjs7m
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