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Endless Love: On the Termination of a Playground Number Game

References [1] Bever, K., Rowlett, J. “Love Games: A Game Theory Approach to Com- patibility”, preprint, arXiv:1312.5483, 2013. [2] Klawe, M., Phillips, E. “A classroom study: Electronic games engage children as researchers”, The first international conference on Computer sup- port for collaborative learning, L. Erlbaum Associates Inc., 209{213, 1995. [3] Papadimitriou, C., Steiglitz, K. Combinatorial optimization: algorithms and complexity, Dover, 1998. [4] Roud, S. The lore of the playground

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Neuro-evolution in Zero-Sum Perfect Information Games on the Android OS

References 1. A. Narayek, Intelligent Agents for Computer Games, Computers and Games Second International Conference, (2000), 414-422 2. C. Kumar and D. Fogel, Evolution, neural networks, games, and Intelligence, Proceedings of the IEEE volume 87 Issue 9, (2000), 1471-1496. 3. M. Buckland, AI Techniques For Game Programming, Premier Press, (2006), 480. 4. K. Stanley, Efficient Evolution of Neural Networks through Complexification, Department of Computer Science University of Texas

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Eternal Picaria

Abstract

Picaria is a traditional board game, played by the Zuni tribe of the American Southwest and other parts of the world, such as a rural Southwest region in Sweden. It is related to the popular children’s game of Tic-tac-toe, but the 2 players have only 3 stones each, and in the second phase of the game, pieces are slided, along specified move edges, in attempts to create the three-in-a-row. We provide a rigorous solution, and prove that the game is a draw; moreover our solution gives insights to strategies that players can use.

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Exploring mod 2 n-queens games

References [1] Bell, J., Stevens, B. “A survey of known results and research areas for n -queens”, Discrete Math. , 309, 1, 1–31, 2009. [2] Bezzel, M. “Proposal of 8-queens problem”, Berliner Schachzeitung , 3, 363, 1848 (submitted under the author name “Schachfreund”). [3] Nauck, F. “Briefwechseln mit allen für alle”, Illustrirte Zeitung , 377, 15, 182, 1850. [4] Noon, H. Surreal Numbers and the N-Queens Game , Master thesis, Bennington College, 2002. [5] Pauls, E. “Das Maximalproblem der Damen auf dem Schachbrete”, Deutsche

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Generalized pairing strategies-a bridge from pairing strategies to colorings

and R. K. Guy, Winning Ways for your mathematical plays , Volume 2 , Academic Press, New York 1982. [6] V. Chvátal and P. Erdős, Biased positional games, Annals of Discrete Math ., 2 (1978), 221–228. [7] A. Csernenszky, The Chooser-Picker 7-in-a-row game. Publicationes Mathematicae , 76 (2010), 431–440. [8] A. Csernenszky, The Picker-Chooser diameter game. Theoretical Computer Science , 411 (2010), 3757–3762. [9] A. Csernenszky, R. Martin and A. Pluhár, On the Complexity of Chooser-Picker Positional Games, Integers , 12 (2012

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Designing Peg Solitaire Puzzles

Abstract

Peg solitaire is an old puzzle with a 300 year history. We consider two ways a computer can be utilized to find interesting peg solitaire puzzles. It is common for a peg solitaire puzzle to begin from a symmetric board position, we have computed solvable symmetric board positions for four board shapes. A new idea is to search for board positions which have a unique starting jump leading to a solution. We show many challenging puzzles uncovered by this search technique. Clever solvers can take advantage of the uniqueness property to help solve these puzzles.

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A Simplified Expression of Share Functions for Cooperative Games with Fuzzy Coalitions

References [1] AUBIN, J. P.: Cooperative fuzzy games, Math. Oper. Res. 6 (1988), 1-13. [2] AUBIN, J. P.: Mathematical Methods of Game and Economic Theory. (Reprint of the 1982 revised ed.), Dover Publ., Mineola, NY, 2007. [3] ALVAREZ-MOZOS, M.-VAN DEN BRINK, R.-VAN DER LAAN, G.-TEJADA, O.: Share functions for cooperative games with levels structure of cooperation, European J. Oper. Res. 244 (2013), 167-179. [4] AUMANN, R. J.-SHAPLEY, L. S.: Values of Non-Atomic Games. Princeton Univ. Press

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Multi Ping-Pong and an Entropy Estimate in Groups

. [6] Langevin R., Walczak P., Some invariants measuring dynamics of codimension-one foliations, in: T. Mizutani et al. (Eds.), Geometric study of foliations,World Sci. Publ., Singapore, 1994, pp. 345-358. [7] Llibre J., Misiurewicz M., Horseshoes, entropy and periods for graph maps, Topology 32 (1993), 649-664. [8] Shi E., Wang S., The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites, Fund. Math. 203 (2009), 21-37. [9] Tarchała K., Walczak P., Ping-pong and

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Universally Kuratowski–Ulam Spaces And Open-Open Games

References [1] Bartoszyński T., Combinatorial aspects of measure and category , Fund. Math. 127 (1987), no. 3, 225–239. [2] Daniels P., Kunen K., Zhou H., On the open-open game , Fund. Math. 145 (1994), no. 3, 205–220. [3] Fremlin D., Natkaniec T., Recław I., Universally Kuratowski–Ulam spaces , Fund. Math. 165 (2000), no. 3, 239–247. [4] Fremlin D., Miller A.W., On some properties of Hurewicz, Menger and Rothberger , Fund. Math. 129 (1988), 17–33. [5] Just W., Miller A.W., Scheepers M., Szeptycki P.J., The combinatorics

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Maximum Genus of the Jenga Like Configurations

Abstract

We treat the boundary of the union of blocks in the Jenga game as a surface with a polyhedral structure and consider its genus. We generalize the game and determine the maximum genus among the configurations in the generalized game.

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