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This study looked at how well digital games helped undergraduate students at the Maulana Azad National Urdu University (MANUU), Hyderabad, Telangana State, India, expand their English vocabulary. Most students indeed own cell phones, laptops, and desktop computers due to the growth of technology and their lower cost. It is common knowledge that most students use their smartphones to play games, which are important for developing their personalities. The researcher promoted the use of digital games in language classes to increase vocabulary and make learning engaging, enjoyable, simple, and efficient. The objective of the study was to determine whether English vocabulary can be taught to undergraduate students in an engaging and effective manner by using digital games to expand students' everyday English vocabulary. The results of this study demonstrated that employing digital games in ESL classes to teach basic English vocabulary is efficient, engaging, and advantageous.

This course surveys research which incorporates psychological evidence into economics. Topics include: prospect theory, biases in probabilistic judgment, self-control and mental accounting with implications for consumption and savings, fairness, altruism, and public goods contributions, financial market anomalies and theories, impact of markets, learning, and incentives, and memory, attention, categorization, and the thinking process.

Pen and paper puzzles are a fun pastime to test your logical reasoning skills, with Sudoku being the most popular of these puzzles. While the problem of solving these puzzles is usually in NP-Complete, generating them is more difficult, depending on the type of puzzle. When generating puzzles for humans, we have to keep in mind how they solve them, as we cannot expect them to brute-force the solution. Generation methods exist for simple number-based puzzles like the Sudoku, but these methods do not translate to the domain of language-based puzzles. We take the concept of strategy-solving to mimic human solving methods and apply them to the Raatsel, a language-based puzzle, and the Sudoku, to generalize a common methodology for generating, solving and rating these problem instances. A new method will be introduced to generate Raatsels using a reduction from Subgraph Isomorphism. This concept of instance generation with specific properties has many applications outside of puzzles, such as validating correctness and generating training data for machine learning., Computer Science

Probability and statistical methods are a better tool for making scientific inferences and handling uncertainty in empirical contexts. We show how the uncertainties happen in inferences and predictions, and how to handle them easily in some cases. Starting with a couple of probability paradoxes, for giving the reader an idea about how tricky the application of the probability can be, a potential uncertainty in statistical significance testing is shown. How the predictions can be done effectively with the probabilistic approach while handing the uncertainties is presented. And finally, what the analyst needs to consider when doing discrete predictions is discussed through application of Simpson’s paradox. For the task effective use of causal assumptions is discussed.

Aquest Treball de Fi de Grau deu el seu nom al seu objectiu principal: abordar l’estudi de la incorporació del Reinforcement Learning als trencaclosques que integren el contingut del treball. En aquest paradigma, els programes aprenen a resoldre problemes matemàticament complexos a partir d'estímuls senzills relacionats amb els seus èxits. Per fer possible el desenvolupament de l’estudi, s'ha implementat la tècnica del Reinforcement Learning com a base i s’ha adaptat a la naturalesa de cada un dels jocs que es tracten. Es fa servir el Q-Learning per a aquells trencaclosques que són possibles d'abordar per la seva capacitat mínimament limitada. En canvi, es contempla el cas d’un joc que no segueix aquesta tendència per marcar una dinàmica massa àmplia. En aquest, s'adaptarà la tècnica de Deep Q-Learning per abordar-ho amb una xarxa neuronal que faciliti la manejabilitat dels estats que formen el trencaclosques. Els resultats que s’han obtingut en aquest estudi reflecteixen que l’aprenentatge d’un model mitjançant estímuls i recompenses en els jocs basats en procediments i regles és totalment assumible. Això s’evidencia ja que l'agent no només aprèn els requisits del joc en qüestió sinó que proporciona la solució òptima respecte a l'elecció de la solució més curta i, per tant, de la minimització d'eleccions errònies. Finalment cal dir que els objectius d’aquest estudi s’han aconseguit satisfactòriament i per comprovar l’aprenentatge, es realitza una comparació del comportament humà amb el del model. Així doncs, s'evidencia la bona integració del camp dels jocs amb la intel·ligència artificial a causa de les regles que regeixen el model de comportament de l’agent., This Final Degree Project owes its name to its main o bjective: einforcement L earning to address the study of the incorporation of Reinforcement Learning in the puzzles that make up the content of the project. In this paradigm, programs learn to solve mathematically complex problems from simple stimuli related to their achievements.To make the development of the project possible, the Reinforcement Learning technique has been implemented as a basis and has been adapted to the nature of each of the games in question. Q Learning is used for those puzzles that are possibl e to address due to their minimally limited capacity. In contrast, the case of a game that does not follow this trend due to have a dynamic that is too broad. In this one, the Deep Qadapted to address it with a neural network th Learning technique will be at facilitates the manageability of the states that make up the game. The results obtained in this project show that model learning through stimuli and rewards in games based on procedures and rules is fully achievable. This is evident since the agent not only learns the requirements of the game in question but also provides the optimal solution regarding the choice of the shortest solution and, therefore, the minimization of erroneous choices. Finally, the objectives of this study have been satisfactoril y achieved and to verify learning, a comparison of human behavior with that of the model is made. Thus, the good integration of the field of games with artificial intelligence is evident due to the rules that govern the behavior model of the agent. II

Pen and paper puzzles are a fun pastime to test your logical reasoning skills, with Sudoku being the most popular of these puzzles. While the problem of solving these puzzles is usually in NP-Complete, generating them is more difficult, depending on the type of puzzle. When generating puzzles for humans, we have to keep in mind how they solve them, as we cannot expect them to brute-force the solution. Generation methods exist for simple number-based puzzles like the Sudoku, but these methods do not translate to the domain of language-based puzzles. We take the concept of strategy-solving to mimic human solving methods and apply them to the Raatsel, a language-based puzzle, and the Sudoku, to generalize a common methodology for generating, solving and rating these problem instances. A new method will be introduced to generate Raatsels using a reduction from Subgraph Isomorphism. This concept of instance generation with specific properties has many applications outside of puzzles, such as validating correctness and generating training data for machine learning., Computer Science

Shikaku is a pencil puzzle consisting of a rectangular grid, with some cells containing a number. The player has to partition the grid into rectangles such that each rectangle contains exactly one number equal to the area of that rectangle. In this paper, we propose two physical zero-knowledge proof protocols for Shikaku using a deck of playing cards, which allow a prover to physically show that he/she knows a solution of the puzzle without revealing it. Most importantly, in our second protocol we develop a general technique to physically verify a rectangle-shaped area with a certain size in a rectangular grid, which can be used to verify other problems with similar constraints.

Gella's Chance by Juan, Kylien, and Bill Wong, is about you taking control of a slime wanting to be a human once more by going in platforming challenges and solving puzzles to get to your goal. Through your adventure you will be encourage and sometimes help by the anonymous Goddess that wants to help you out, but only in messages she leaves. The game is a more laidback and doesn't really have a serious story it just wants you to have fun and explore the levels you are place in to solve and move around using the three elements of Fire, Ice, Earth, and of course your normal gelatinous form.

[ES] “On the Tracks” es un proyecto de emprendimiento en el marco de la start.inf que nace en la asignatura de Introducción a la Programación de Videojuegos, de la mano de tres estudiantes de la ETSINF. El juego, con un aspecto gráfico low poly en 3D, combina mecánicas de resolución de puzles y de combates permitiendo así que el jugador tenga la posibilidad de elegir su propia experiencia de juego. El grupo está compuesto por: Alberto Baixauli Herráez, encargado del desarrollo e implementación de los niveles de puzles; Carlos Enrique Pérez Cobas, el cual ya no forma parte del proyecto, se encargó de la integración de las animaciones y de la creación de las primeras versiones de la mecánica de combate y Carlos Martínez Jiménez, encargado de implementar nuevas mecánicas y niveles de combate, así como mejorar los actuales. Este TFG está planteado de tal forma que sirva de guía para mostrar todo el desarrollo pertinente a las mecánicas necesarias para la resolución de puzles asociadas al videojuego “On the Track”. Hablaremos por tanto de las propias mecánicas, sus usos y posibles combinaciones. También se definirá todo lo relacionado con dichas mecánicas como puede ser animaciones, efectos visuales y sonoros. Además, debido a que la naturaleza del videojuego también incluye una faceta de combate, se deberán integrar conjuntamente para mejorar la experiencia del usuario y evitar que la experiencia de juego se vea dañada., [EN] “On the Tracks” is an entrepreneurial project within the framework of start.inf that was born during Introduction to Video Game Programming, by three ETSINF students. The game, with a low poly 3D graphic aspect, combines puzzle solving and combat mechanics, thus allowing the player to choose their own gaming experience. The group is made up of: Alberto Baixauli Herráez, in charge of the development and implementation of the puzzle levels; Carlos Enrique Pérez Cobas, who is no longer part of the project, who oversaw integrating the animations and creating the first versions of the combat mechanics and Carlos Martínez Jiménez, in charge of implementing new mechanics and combat levels, as well as improving the current ones. This TFG is designed to serve as a guide to show the development and programming of the mechanics necessary for solving puzzles presented in the game “On the Track”. We will therefore talk about the mechanics themselves, their uses, and possible combinations. Everything related to these mechanics will also be defined, such as animations, visual and sound effects. In addition, in this TFG, we must ensure that the mechanics implemented are integrated with the combat facet of “On the Track” to avoid that the game experience is ruined.

[ES] Este trabajo de fin de grado recoge la documentación sobre la contextualización, preproducción, producción y postproducción de un prototipo jugable de videojuego serio 2D híbrido entre plataformas y puzles de desarrollo personal. En concreto se presentan los procesos de contextualización, ideación, diseño de la narrativa interactiva (argumento, personajes, niveles, mecánicas, mapas e interfaz) junto a la memoria del desarrollo técnico del prototipo jugable., [EN] This final degree project gathers the documentation about the contextualization, preproduction, production, and postproduction of a playable prototype of a 2D serious videogame, which mixes platform and puzzle genre with a personal growth theme. Specifically, it presents the processes of contextualization, ideation, interactive narrative design (story line, characters, game levels, mechanics, maps, and interface) along with a technical development memory of the playable prototype.

[ES] “On the Tracks” es un proyecto de emprendimiento en el marco de la start.inf que nace en la asignatura de Introducción a la Programación de Videojuegos, de la mano de tres estudiantes de la ETSINF. El juego, con un aspecto gráfico low poly en 3D, combina mecánicas de resolución de puzles y de combates permitiendo así que el jugador tenga la posibilidad de elegir su propia experiencia de juego. El grupo está compuesto por: Alberto Baixauli Herráez, encargado del desarrollo e implementación de los niveles de puzles; Carlos Enrique Pérez Cobas, el cual ya no forma parte del proyecto, se encargó de la integración de las animaciones y de la creación de las primeras versiones de la mecánica de combate y Carlos Martínez Jiménez, encargado de implementar nuevas mecánicas y niveles de combate, así como mejorar los actuales. Este TFG está planteado de tal forma que sirva de guía para mostrar todo el desarrollo pertinente a las mecánicas necesarias para la resolución de puzles asociadas al videojuego “On the Track”. Hablaremos por tanto de las propias mecánicas, sus usos y posibles combinaciones. También se definirá todo lo relacionado con dichas mecánicas como puede ser animaciones, efectos visuales y sonoros. Además, debido a que la naturaleza del videojuego también incluye una faceta de combate, se deberán integrar conjuntamente para mejorar la experiencia del usuario y evitar que la experiencia de juego se vea dañada., [EN] “On the Tracks” is an entrepreneurial project within the framework of start.inf that was born during Introduction to Video Game Programming, by three ETSINF students. The game, with a low poly 3D graphic aspect, combines puzzle solving and combat mechanics, thus allowing the player to choose their own gaming experience. The group is made up of: Alberto Baixauli Herráez, in charge of the development and implementation of the puzzle levels; Carlos Enrique Pérez Cobas, who is no longer part of the project, who oversaw integrating the animations and creating the first versions of the combat mechanics and Carlos Martínez Jiménez, in charge of implementing new mechanics and combat levels, as well as improving the current ones. This TFG is designed to serve as a guide to show the development and programming of the mechanics necessary for solving puzzles presented in the game “On the Track”. We will therefore talk about the mechanics themselves, their uses, and possible combinations. Everything related to these mechanics will also be defined, such as animations, visual and sound effects. In addition, in this TFG, we must ensure that the mechanics implemented are integrated with the combat facet of “On the Track” to avoid that the game experience is ruined.

[ES] Este trabajo de fin de grado recoge la documentación sobre la contextualización, preproducción, producción y postproducción de un prototipo jugable de videojuego serio 2D híbrido entre plataformas y puzles de desarrollo personal. En concreto se presentan los procesos de contextualización, ideación, diseño de la narrativa interactiva (argumento, personajes, niveles, mecánicas, mapas e interfaz) junto a la memoria del desarrollo técnico del prototipo jugable., [EN] This final degree project gathers the documentation about the contextualization, preproduction, production, and postproduction of a playable prototype of a 2D serious videogame, which mixes platform and puzzle genre with a personal growth theme. Specifically, it presents the processes of contextualization, ideation, interactive narrative design (story line, characters, game levels, mechanics, maps, and interface) along with a technical development memory of the playable prototype.

[ES] Este trabajo de fin de grado recoge la documentación sobre la contextualización, preproducción, producción y postproducción de un prototipo jugable de videojuego serio 2D híbrido entre plataformas y puzles de desarrollo personal. En concreto se presentan los procesos de contextualización, ideación, diseño de la narrativa interactiva (argumento, personajes, niveles, mecánicas, mapas e interfaz) junto a la memoria del desarrollo técnico del prototipo jugable., [EN] This final degree project gathers the documentation about the contextualization, preproduction, production, and postproduction of a playable prototype of a 2D serious videogame, which mixes platform and puzzle genre with a personal growth theme. Specifically, it presents the processes of contextualization, ideation, interactive narrative design (story line, characters, game levels, mechanics, maps, and interface) along with a technical development memory of the playable prototype.

[ES] Este trabajo de fin de grado recoge la documentación sobre la contextualización, preproducción, producción y postproducción de un prototipo jugable de videojuego serio 2D híbrido entre plataformas y puzles de desarrollo personal. En concreto se presentan los procesos de contextualización, ideación, diseño de la narrativa interactiva (argumento, personajes, niveles, mecánicas, mapas e interfaz) junto a la memoria del desarrollo técnico del prototipo jugable., [EN] This final degree project gathers the documentation about the contextualization, preproduction, production, and postproduction of a playable prototype of a 2D serious videogame, which mixes platform and puzzle genre with a personal growth theme. Specifically, it presents the processes of contextualization, ideation, interactive narrative design (story line, characters, game levels, mechanics, maps, and interface) along with a technical development memory of the playable prototype.

Gella's Chance by Juan, Kylien, and Bill Wong, is about you taking control of a slime wanting to be a human once more by going in platforming challenges and solving puzzles to get to your goal. Through your adventure you will be encourage and sometimes help by the anonymous Goddess that wants to help you out, but only in messages she leaves. The game is a more laidback and doesn't really have a serious story it just wants you to have fun and explore the levels you are place in to solve and move around using the three elements of Fire, Ice, Earth, and of course your normal gelatinous form.

Here, we observed 3- to 4-year-old children (N=31) and their parents playing with puzzles at home during a zoom session to provide insight into the variability of the kinds of puzzles children have in their home, and the variability in how children and their parents play with spatial toys. We observed a large amount of variability in both children and parents' behaviors, and in the puzzles they selected. Further, we found relations between parents' and children's behaviors. For example, parents provided more scaffolding behaviors for younger children and parents' persistence-focused language was related to more child attempts after failure. Altogether, the present work shows how using methods of observing children at a distance, we can gain insight into the environment in which they are developing. The results are discussed in terms of how variability in spatial toys and spatial play during naturalistic interactions can help us contextualize the conclusions we draw from lab-based studies.

Cada vegada són més comuns els casos d'agressions sexuals a persones amb discapacitats intel·lectuals. Aprofitant el fet que aquest col·lectiu sovint se sent molt atret pels videojocs, ens vam plantejar crear un videojoc per a promocionar les diferents parts de l'educació social, afectiva i sexual, per tal d'aportar coneixements i promoure actituds que poden ajudar-los en aquests aspectes i evitar situacions de risc. Per tant, aquest projecte neix tractant de cobrir aquest problema. Es tracta d'un videojoc on l'usuari haurà de completar els diferents nivells (puzles de tota mena) per obtenir recompenses i aprendre, acompanyat d'un guia durant tota l'aventura. El disseny d'aquest videojoc ha estat supervisat per una terapeuta ocupacional, per tal d'aportar els coneixements necessaris d'una manera agradable i divertida. Per a desenvolupar aquest projecte s'ha seguit una metodologia Agile adaptada a un equip d'un únic desenvolupador i una terapeuta. S'ha utilitzat el motor Unity per al desenvolupament principal del videojoc. El projecte ha complert amb tots els objectius establerts i ha servit per consolidar els coneixements sobre sistemes software i videojocs. Una primera avaluació del videojoc, mitjançant un estudi d'usuari amb persones amb discapacitats intel·lectuals, mostra uns resultats molt encoratjadors., Cases of sexual assault on people with intellectual disabilities are becoming more common. So knowing that this group is very attracted to video games, why not create a video game to promote the different parts of social, emotional and sexual education? Therefore, this project is born trying to cover this problem. This is a video game where the user will have to complete the different levels (puzzles of all kinds) to get rewards and learn, this will be accompanied by a guide throughout the adventure. The design of this video game has been supervised by an occupational therapist, in order to provide the necessary knowledge in a pleasant and fun way. To develop this project, an Agile methodology adapted to a team of a single developer and a therapist was followed. The Unity engine was used for the main development of the video game. Finally, the project has met all the established objectives and has served to consolidate knowledge about software systems and video games., Cada vez son más comunes los casos de agresiones sexuales a personas con discapacidad intelectual. Sabiendo pues que este colectivo se siente muy atraído por los videojuegos, ¿por qué no crear un videojuego para promocionar las diferentes partes de la educación social, afectiva y sexual? Por lo tanto, este proyecto nace tratando de cubrir este problema. Se trata de un videojuego donde el usuario deberá completar los diferentes niveles (puzzles de todo tipo) para obtener recompensas y aprender, esto lo hará acompañado de un guía durante toda la aventura. El diseño de este videojuego ha sido supervisado por una terapeuta ocupacional, con el fin de aportar los conocimientos necesarios de una manera agradable y divertida. Para desarrollar este proyecto se ha seguido una metodología Agile adaptada a un equipo de un único desarrollador y una terapeuta. Se ha utilizado el motor Unity para el desarrollo principal del videojuego. Finalmente pues, el proyecto ha cumplido con todos los objetivos establecidos y ha servido para consolidar los conocimientos sobre sistemas software y videojuegos

[ES] En este proyecto Fin de grado se desarrollará una colección de juegos de ingenio relacionados con el consumo de vino para un público adulto. Estos juegos de ingenio funcionan de tal forma que, al colocarlos en una botella de vino, estos impiden la apertura de la botella hasta que no sean resueltos, funcionando como un ¿candado¿ para botellas de vino. Estos juegos pretender ser un objeto que genere diálogo, creando durante el consumo de vino un ambiente propicio para la socialización permitiendo a los usuarios entretenerse con el desafío y pasar un rato ameno mientras intentan liberar la botella de vino. Está pensado para amantes del vino que también disfrutan de los juegos de ingenio. Estos puzles han sido diseñados para su fabricación mediante el proceso de impresión 3D., [EN] This project will develop a collection of puzzles related to wine consumption for an adult audience. These puzzles work in such a way that, when placed in a bottle of wine, they prevent the opening of the bottle until they are resolved, working as a "lock" for wine bottles. These games pretend to be an object that generates dialogue, creating during the consumption of wine an environment conducive to socialization allowing users to be entertained with the challenge and have a fun time while trying to free the bottle of wine. It is designed for wine lovers who also enjoy witty games. These puzzles will be designed to be manufactured through the 3D printing process., [CA] En aquest projecte Fi de grau es desenvoluparà una col·lecció de jocs d'enginy relacionats amb el consum de vi per a un públic adult. Aquests jocs d'enginy funcionen de tal manera que, a l'col·locar-los en una ampolla de vi, aquests impedeixen l'obertura de l'ampolla fins que no siguin resolts, funcionant com un "cadenat" per a ampolles de vi. Aquests jocs pretendre ser un objecte que generi diàleg, creant durant el consum de vi un ambient propici per a la socialització permetent als usuaris entretenir-se amb el desafiament i passar una estona amena mentre intenten alliberar l'ampolla de vi. Està pensat per a amants de el vi que també gaudeixen dels jocs d'enginy. Aquests puzles han estat dissenyats per a la seva fabricació mitjançant el procés d'impressió 3D.

[ES] En este proyecto Fin de grado se desarrollará una colección de juegos de ingenio relacionados con el consumo de vino para un público adulto. Estos juegos de ingenio funcionan de tal forma que, al colocarlos en una botella de vino, estos impiden la apertura de la botella hasta que no sean resueltos, funcionando como un ¿candado¿ para botellas de vino. Estos juegos pretender ser un objeto que genere diálogo, creando durante el consumo de vino un ambiente propicio para la socialización permitiendo a los usuarios entretenerse con el desafío y pasar un rato ameno mientras intentan liberar la botella de vino. Está pensado para amantes del vino que también disfrutan de los juegos de ingenio. Estos puzles han sido diseñados para su fabricación mediante el proceso de impresión 3D., [EN] This project will develop a collection of puzzles related to wine consumption for an adult audience. These puzzles work in such a way that, when placed in a bottle of wine, they prevent the opening of the bottle until they are resolved, working as a "lock" for wine bottles. These games pretend to be an object that generates dialogue, creating during the consumption of wine an environment conducive to socialization allowing users to be entertained with the challenge and have a fun time while trying to free the bottle of wine. It is designed for wine lovers who also enjoy witty games. These puzzles will be designed to be manufactured through the 3D printing process., [CA] En aquest projecte Fi de grau es desenvoluparà una col·lecció de jocs d'enginy relacionats amb el consum de vi per a un públic adult. Aquests jocs d'enginy funcionen de tal manera que, a l'col·locar-los en una ampolla de vi, aquests impedeixen l'obertura de l'ampolla fins que no siguin resolts, funcionant com un "cadenat" per a ampolles de vi. Aquests jocs pretendre ser un objecte que generi diàleg, creant durant el consum de vi un ambient propici per a la socialització permetent als usuaris entretenir-se amb el desafiament i passar una estona amena mentre intenten alliberar l'ampolla de vi. Està pensat per a amants de el vi que també gaudeixen dels jocs d'enginy. Aquests puzles han estat dissenyats per a la seva fabricació mitjançant el procés d'impressió 3D.

4 heroes wake up with no memories and must navigate their own adversities to get back their memories and defeat The Lich!

[ES] En este proyecto Fin de grado se desarrollará una colección de juegos de ingenio relacionados con el consumo de vino para un público adulto. Estos juegos de ingenio funcionan de tal forma que, al colocarlos en una botella de vino, estos impiden la apertura de la botella hasta que no sean resueltos, funcionando como un ¿candado¿ para botellas de vino. Estos juegos pretender ser un objeto que genere diálogo, creando durante el consumo de vino un ambiente propicio para la socialización permitiendo a los usuarios entretenerse con el desafío y pasar un rato ameno mientras intentan liberar la botella de vino. Está pensado para amantes del vino que también disfrutan de los juegos de ingenio. Estos puzles han sido diseñados para su fabricación mediante el proceso de impresión 3D., [EN] This project will develop a collection of puzzles related to wine consumption for an adult audience. These puzzles work in such a way that, when placed in a bottle of wine, they prevent the opening of the bottle until they are resolved, working as a "lock" for wine bottles. These games pretend to be an object that generates dialogue, creating during the consumption of wine an environment conducive to socialization allowing users to be entertained with the challenge and have a fun time while trying to free the bottle of wine. It is designed for wine lovers who also enjoy witty games. These puzzles will be designed to be manufactured through the 3D printing process., [CA] En aquest projecte Fi de grau es desenvoluparà una col·lecció de jocs d'enginy relacionats amb el consum de vi per a un públic adult. Aquests jocs d'enginy funcionen de tal manera que, a l'col·locar-los en una ampolla de vi, aquests impedeixen l'obertura de l'ampolla fins que no siguin resolts, funcionant com un "cadenat" per a ampolles de vi. Aquests jocs pretendre ser un objecte que generi diàleg, creant durant el consum de vi un ambient propici per a la socialització permetent als usuaris entretenir-se amb el desafiament i passar una estona amena mentre intenten alliberar l'ampolla de vi. Està pensat per a amants de el vi que també gaudeixen dels jocs d'enginy. Aquests puzles han estat dissenyats per a la seva fabricació mitjançant el procés d'impressió 3D.

4 heroes wake up with no memories and must navigate their own adversities to get back their memories and defeat The Lich!

We discuss some results on the complexity of games and puzzles. In particular, we focus on the relationship between bounded treewidth and the (in-)tractability of games and puzzles in which graphs play a role. We discuss some general methods which are good starting points for finding complexity proofs for games and puzzles.

Numberlink is a logic puzzle for which the player has to connect all pairs of cells with the same numbers by non-crossing paths in a rectangular grid. In this paper, we propose a physical protocol of zero-knowledge proof for Numberlink using a deck of cards, which allows a player to physically show that he/she knows a solution without revealing it. In particular, we develop a physical protocol to count the number of elements in a list that are equal to a given secret value without revealing that value, the positions of elements in the list that are equal to it, or the value of any other element in the list. Our protocol can also be applied to verify the existence of vertex-disjoint paths connecting all given pairs of endpoints in any undirected graph.

Consider n²-1 unit-square blocks in an n × n square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable - a variation of Rush Hour with only 1 × 1 cars and fixed blocks. We prove that it is PSPACE-complete to decide whether a given block can reach the left edge of the board, by reduction from Nondeterministic Constraint Logic via 2-color oriented Subway Shuffle. By contrast, polynomial-time algorithms are known for deciding whether a given block can be moved by one space, or when each block either is immovable or can move both horizontally and vertically. Our result answers a 15-year-old open problem by Tromp and Cilibrasi, and strengthens previous PSPACE-completeness results for Rush Hour with vertical 1 × 2 and horizontal 2 × 1 movable blocks and 4-color Subway Shuffle.

Speaking is one of the basic language skills that students should master in order to communicate effectively and interact with others. Speaking skills are necessary for the social as well as academic life of a person by becoming responsive as well as receptive to information thus forming a favorable impression of oneself. Internationally, there is a debate that several high school graduates cannot properly speak English language and even the bright learners who get high scores in written tests cannot express themselves verbally, despite English being the official language of instruction in these schools Language learning is a hard task and it requires extraordinary efforts to realize the desirable outcomes. Language games are techniques and procedures that may be used by instructors to improve the speaking skills. Accordingly, the main objective of this study was to establish the effect of language games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. Specifically, the study sought to establish the effect of role plays, problem-solving, puzzles, and board race games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. The research was an empirical analysis and thus adopted an empirical research design and content analysis was used in the analysis of the qualitative data. The study revealed that language games significantly influence the acquisition of the speaking skills of the students. The study further found that using language games in teaching enhances the students’ achievement and results of speaking skills. Students enjoyed their lesson and got more motivation, interest, and confidence when learning is based on the use of language games. Hence, language games should be used as designed activities in teaching speaking skills. The study findings were generalized to students of Junior High School in Hohoe Municipality in Ghana, who like many other students in

Speaking is one of the basic language skills that students should master in order to communicate effectively and interact with others. Speaking skills are necessary for the social as well as academic life of a person by becoming responsive as well as receptive to information thus forming a favorable impression of oneself. Internationally, there is a debate that several high school graduates cannot properly speak English language and even the bright learners who get high scores in written tests cannot express themselves verbally, despite English being the official language of instruction in these schools Language learning is a hard task and it requires extraordinary efforts to realize the desirable outcomes. Language games are techniques and procedures that may be used by instructors to improve the speaking skills. Accordingly, the main objective of this study was to establish the effect of language games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. Specifically, the study sought to establish the effect of role plays, problem-solving, puzzles, and board race games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. The research was an empirical analysis and thus adopted an empirical research design and content analysis was used in the analysis of the qualitative data. The study revealed that language games significantly influence the acquisition of the speaking skills of the students. The study further found that using language games in teaching enhances the students’ achievement and results of speaking skills. Students enjoyed their lesson and got more motivation, interest, and confidence when learning is based on the use of language games. Hence, language games should be used as designed activities in teaching speaking skills. The study findings were generalized to students of Junior High School in Hohoe Municipality in Ghana, who like many other students in

Speaking is one of the basic language skills that students should master in order to communicate effectively and interact with others. Speaking skills are necessary for the social as well as academic life of a person by becoming responsive as well as receptive to information thus forming a favorable impression of oneself. Internationally, there is a debate that several high school graduates cannot properly speak English language and even the bright learners who get high scores in written tests cannot express themselves verbally, despite English being the official language of instruction in these schools Language learning is a hard task and it requires extraordinary efforts to realize the desirable outcomes. Language games are techniques and procedures that may be used by instructors to improve the speaking skills. Accordingly, the main objective of this study was to establish the effect of language games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. Specifically, the study sought to establish the effect of role plays, problem-solving, puzzles, and board race games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. The research was an empirical analysis and thus adopted an empirical research design and content analysis was used in the analysis of the qualitative data. The study revealed that language games significantly influence the acquisition of the speaking skills of the students. The study further found that using language games in teaching enhances the students’ achievement and results of speaking skills. Students enjoyed their lesson and got more motivation, interest, and confidence when learning is based on the use of language games. Hence, language games should be used as designed activities in teaching speaking skills. The study findings were generalized to students of Junior High School in Hohoe Municipality in Ghana, who like many other students in

Speaking is one of the basic language skills that students should master in order to communicate effectively and interact with others. Speaking skills are necessary for the social as well as academic life of a person by becoming responsive as well as receptive to information thus forming a favorable impression of oneself. Internationally, there is a debate that several high school graduates cannot properly speak English language and even the bright learners who get high scores in written tests cannot express themselves verbally, despite English being the official language of instruction in these schools Language learning is a hard task and it requires extraordinary efforts to realize the desirable outcomes. Language games are techniques and procedures that may be used by instructors to improve the speaking skills. Accordingly, the main objective of this study was to establish the effect of language games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. Specifically, the study sought to establish the effect of role plays, problem-solving, puzzles, and board race games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. The research was an empirical analysis and thus adopted an empirical research design and content analysis was used in the analysis of the qualitative data. The study revealed that language games significantly influence the acquisition of the speaking skills of the students. The study further found that using language games in teaching enhances the students’ achievement and results of speaking skills. Students enjoyed their lesson and got more motivation, interest, and confidence when learning is based on the use of language games. Hence, language games should be used as designed activities in teaching speaking skills. The study findings were generalized to students of Junior High School in Hohoe Municipality in Ghana, who like many other students in

En este trabajo se aplicará la tecnología de impresión en 3D a una estructura modulable. Se ha elegido como estructura modulable los puzzles secuenciales, en concreto un cubo de rubik convencional. El motivo de estudio de esta estructura modulable es para poder realizar prototipos de los diferentes puzzles secuenciales con el fin de mejorar la fase de diseño de los mismos. Los puzzles secuenciales se producen con el método de moldeo por inyección. Este método es muy rápido, pero no siempre se producen puzzles de la calidad que se desea. Debido a que la indústria es pequeña y no tiene requerimientos de seguridad especiales más que cualquier otro juguete común, no se realizan simulaciones estructurales y no se pueden controlar posibles errores. La impresión en tres dimensiones es una herramienta fundamental hoy en día para la generación de prototipos para muchas empresas y se podría aplicar al diseño de puzzles secuenciales para evitar casos como el del DaYan PanShi. Últimamente muchos puzzles secuenciales nuevos se producen con métodos de impresión en 3D ya que su producción en masa no es viable, ya sea por las limitadas posibilidades del moldeo por inyección o por no ser viables económicamente. Para evitar el problema con los puzzles con un diseño pobre, antes de generar los moldes de inyección, se comprobaría la estructura de manera experimental, ya que es factible imprimir las piezas en materiales similares o incluso idénticos a los del moldeo por inyección. Además de poder predecir el comportamiento mecánico del puzzle en el caso que se deba a la estructura y no al acabado. En caso de superar las pruebas se pasa a producir los moldes y a producir. En caso contrario se vuelve al proceso de diseño para mejorar las partes que fallan. Después del diseño y su impresión, hemos obtenido un producto que no cumple las espectativas. Las esquinas, la pieza que más tiende a fallar por su diseño y por las fuerzas que soporta, ha fallado. El acabado no es suficientemente liso

Speaking is one of the basic language skills that students should master in order to communicate effectively and interact with others. Speaking skills are necessary for the social as well as academic life of a person by becoming responsive as well as receptive to information thus forming a favorable impression of oneself. Internationally, there is a debate that several high school graduates cannot properly speak English language and even the bright learners who get high scores in written tests cannot express themselves verbally, despite English being the official language of instruction in these schools Language learning is a hard task and it requires extraordinary efforts to realize the desirable outcomes. Language games are techniques and procedures that may be used by instructors to improve the speaking skills. Accordingly, the main objective of this study was to establish the effect of language games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. Specifically, the study sought to establish the effect of role plays, problem-solving, puzzles, and board race games on acquisition of speaking skills among students of Junior High School in Hohoe Municipality in Ghana. The research was an empirical analysis and thus adopted an empirical research design and content analysis was used in the analysis of the qualitative data. The study revealed that language games significantly influence the acquisition of the speaking skills of the students. The study further found that using language games in teaching enhances the students’ achievement and results of speaking skills. Students enjoyed their lesson and got more motivation, interest, and confidence when learning is based on the use of language games. Hence, language games should be used as designed activities in teaching speaking skills. The study findings were generalized to students of Junior High School in Hohoe Municipality in Ghana, who like many other students in

[EN] My Final Degree project consists on designing a 2D platform and puzzle videogame whose title is Crystal Fate. I will be focused on the artistic and gameplay design development. In order to reinforce the different possibilities for gameplaying I will start with a theoretical study about those two kinds of game, and from other videogames that have served as a reference for my story and gameplay mechanics. After the theoretical study I start working on the idea, drawing some characters sketches, concept art and animations. At the end of the process I will have generated the stuff needed to create a playable prototype., [ES] Mi trabajo de final de grado consiste en la creación de un videojuego 2D, de género plataforma y puzle llamado Crystal Fate, abarcando su desarrollo tanto artístico, como de diseño de niveles y mecánicas de juego. Para conocer mejor las distintas posibilidades que puede ofrecer el juego se hará un estudio teórico de estos dos géneros y de algunos videojuegos referenciales, tanto de inspiración para el argumento como de sus mecánicas. Tras terminar esta parte del estudio me dispondré a pasar a la fase de desarrollo de la idea mediante la creación de bocetos de los diferentes personajes, concept art y animaciones. Como resultado final de este proyecto se tendrá el material necesario para realizar un pequeño prototipo y poder ver el videojuego en acción.

[EN] My Final Degree project consists on designing a 2D platform and puzzle videogame whose title is Crystal Fate. I will be focused on the artistic and gameplay design development. In order to reinforce the different possibilities for gameplaying I will start with a theoretical study about those two kinds of game, and from other videogames that have served as a reference for my story and gameplay mechanics. After the theoretical study I start working on the idea, drawing some characters sketches, concept art and animations. At the end of the process I will have generated the stuff needed to create a playable prototype., [ES] Mi trabajo de final de grado consiste en la creación de un videojuego 2D, de género plataforma y puzle llamado Crystal Fate, abarcando su desarrollo tanto artístico, como de diseño de niveles y mecánicas de juego. Para conocer mejor las distintas posibilidades que puede ofrecer el juego se hará un estudio teórico de estos dos géneros y de algunos videojuegos referenciales, tanto de inspiración para el argumento como de sus mecánicas. Tras terminar esta parte del estudio me dispondré a pasar a la fase de desarrollo de la idea mediante la creación de bocetos de los diferentes personajes, concept art y animaciones. Como resultado final de este proyecto se tendrá el material necesario para realizar un pequeño prototipo y poder ver el videojuego en acción.

[EN] My Final Degree project consists on designing a 2D platform and puzzle videogame whose title is Crystal Fate. I will be focused on the artistic and gameplay design development. In order to reinforce the different possibilities for gameplaying I will start with a theoretical study about those two kinds of game, and from other videogames that have served as a reference for my story and gameplay mechanics. After the theoretical study I start working on the idea, drawing some characters sketches, concept art and animations. At the end of the process I will have generated the stuff needed to create a playable prototype., [ES] Mi trabajo de final de grado consiste en la creación de un videojuego 2D, de género plataforma y puzle llamado Crystal Fate, abarcando su desarrollo tanto artístico, como de diseño de niveles y mecánicas de juego. Para conocer mejor las distintas posibilidades que puede ofrecer el juego se hará un estudio teórico de estos dos géneros y de algunos videojuegos referenciales, tanto de inspiración para el argumento como de sus mecánicas. Tras terminar esta parte del estudio me dispondré a pasar a la fase de desarrollo de la idea mediante la creación de bocetos de los diferentes personajes, concept art y animaciones. Como resultado final de este proyecto se tendrá el material necesario para realizar un pequeño prototipo y poder ver el videojuego en acción.

Snake and Nibbler are two well-known video games in which a snake slithers through a maze and grows as it collects food. During this process, the snake must avoid any collision with its tail. Various goals can be associated with these video games, such as avoiding the tail as long as possible, or collecting a certain amount of food, or reaching some target location. Unfortunately, like many other motion-planning problems, even very restricted variants are computationally intractable. In particular, we prove the NP-hardness of collecting all food on solid grid graphs; as well as its PSPACE-completeness on general grid graphs. Moreover, given an initial and a target configuration of the snake, moving from one configuration to the other is PSPACE-complete, even on grid graphs without food, or with an initially short snake. Our results make use of the nondeterministic constraint logic framework by Hearn and Demaine, which has been used to analyze the computational complexity of many games and puzzles. We extend this framework for the analysis of puzzles whose initial state is chosen by the player.

Escape rooms are an emerging market. In these physical and mostly group based games, players are locked in a room with the goal to solve puzzles within a certain time limit in order to ’escape’ the room. To make sure players have a pleasurable experience, they are monitored during the game by a so called game master. This person helps players during the game. When players get stuck the game master gives players a hint. Another possible task of the game master is to create an immersive story within the escape room. The game master can do this by communicating with the players while taking on the role of certain characters that are part of that story. The goal of this project was to develop the Escape-Master system: a system that automates the role of the game master. In the system the game master can define an arbitrary escape room by inputting puzzles, characters and dialog for those characters. This dialog can include hints or storyline narrative. With this information provided, the system can automatically interact with the players. The system keeps track of the progress of the players and uses this information to interpret questions they provide to the system using natural language processing. After this the system can provide a fitting response, which can be a hint or narrative that progresses the story of the escape room. The system can also start interactions with players on its own, based on time passed of their progress in the game. The project consisted of two phases: research and development. During the research phase information was gathered on player interaction, user engagement, and chatbots. During the development phase a system was constructed that permits the game master automate the process of giving hints and create an immersive story. Additionally, an interface was build to give the game master the ability to define an escape room and start games while being notified of the actions the system takes. It was tested in a live setting on two o, Bachelor End Project, Computer Science

In this thesis we analyze the role of puzzles in blockchain based distributed systems. We extract the relevant properties from existing puzzle mechanisms and use them to define an abstract notion for proof-of-work puzzles. The resulting puzzles have exponentially distributed solving time and allow to consider nodes and parties with individual solving capabilities. We use the new definition of proof-of-work puzzles in a bottom-up construction of a blockchain protocol. Our new model is compatible with the Bitcoin backbone protocol, in the sense that we can transfer the backbone protocol’s properties to our model. During the construction we try to pinpoint the original design decisions made for Bitcoin., Patrik Keller, Masterarbeit University of Innsbruck 2018

In this thesis we analyze the role of puzzles in blockchain based distributed systems. We extract the relevant properties from existing puzzle mechanisms and use them to define an abstract notion for proof-of-work puzzles. The resulting puzzles have exponentially distributed solving time and allow to consider nodes and parties with individual solving capabilities. We use the new definition of proof-of-work puzzles in a bottom-up construction of a blockchain protocol. Our new model is compatible with the Bitcoin backbone protocol, in the sense that we can transfer the backbone protocol’s properties to our model. During the construction we try to pinpoint the original design decisions made for Bitcoin., Patrik Keller, Masterarbeit University of Innsbruck 2018

Snake and Nibbler are two well-known video games in which a snake slithers through a maze and grows as it collects food. During this process, the snake must avoid any collision with its tail. Various goals can be associated with these video games, such as avoiding the tail as long as possible, or collecting a certain amount of food, or reaching some target location. Unfortunately, like many other motion-planning problems, even very restricted variants are computationally intractable. In particular, we prove the NP-hardness of collecting all food on solid grid graphs; as well as its PSPACE-completeness on general grid graphs. Moreover, given an initial and a target configuration of the snake, moving from one configuration to the other is PSPACE-complete, even on grid graphs without food, or with an initially short snake. Our results make use of the nondeterministic constraint logic framework by Hearn and Demaine, which has been used to analyze the computational complexity of many games and puzzles. We extend this framework for the analysis of puzzles whose initial state is chosen by the player.

Escape rooms are an emerging market. In these physical and mostly group based games, players are locked in a room with the goal to solve puzzles within a certain time limit in order to ’escape’ the room. To make sure players have a pleasurable experience, they are monitored during the game by a so called game master. This person helps players during the game. When players get stuck the game master gives players a hint. Another possible task of the game master is to create an immersive story within the escape room. The game master can do this by communicating with the players while taking on the role of certain characters that are part of that story. The goal of this project was to develop the Escape-Master system: a system that automates the role of the game master. In the system the game master can define an arbitrary escape room by inputting puzzles, characters and dialog for those characters. This dialog can include hints or storyline narrative. With this information provided, the system can automatically interact with the players. The system keeps track of the progress of the players and uses this information to interpret questions they provide to the system using natural language processing. After this the system can provide a fitting response, which can be a hint or narrative that progresses the story of the escape room. The system can also start interactions with players on its own, based on time passed of their progress in the game. The project consisted of two phases: research and development. During the research phase information was gathered on player interaction, user engagement, and chatbots. During the development phase a system was constructed that permits the game master automate the process of giving hints and create an immersive story. Additionally, an interface was build to give the game master the ability to define an escape room and start games while being notified of the actions the system takes. It was tested in a live setting on two o, Bachelor End Project, Computer Science

We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a path in a rectangular grid graph from a start vertex to a destination vertex. The different puzzle types place different constraints on the path: preventing some edges from being visited (broken edges); forcing some edges or vertices to be visited (hexagons); forcing some cells to have certain numbers of incident path edges (triangles); or forcing the regions formed by the path to be partially monochromatic (squares), have exactly two special cells (stars), or be singly covered by given shapes (polyominoes) and/or negatively counting shapes (antipolyominoes). We show that any one of these clue types (except the first) is enough to make path finding NP-complete ("witnesses exist but are hard to find"), even for rectangular boards. Furthermore, we show that a final clue type (antibody), which necessarily "cancels" the effect of another clue in the same region, makes path finding Sigma_2-complete ("witnesses do not exist"), even with a single antibody (combined with many anti/polyominoes), and the problem gets no harder with many antibodies.

We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change the state. This type of setup is common to many robot motion planning hardness proofs. We characterize the complexity for a natural simple case: each gadget connects up to four locations in a perfect matching (but each direction can be traversable or not in the current state), has one or two states, every gadget traversal is immediately undoable, and that gadget locations are connected by an always-traversable forest, possibly restricted to avoid crossings in the plane. Specifically, we show that any single nontrivial four-location two-state gadget type is enough for motion planning to become PSPACE-complete, while any set of simpler gadgets (effectively two-location or one-state) has a polynomial-time motion planning algorithm. As a sample application, our results show that motion planning games with "spinners" are PSPACE-complete, establishing a new hard aspect of Zelda: Oracle of Seasons.

[EN] In this paper we show how to model and to analyse the solubility of some puzzles, brainteasers and other mathematical toys. We make use of basic group theory concepts and the computational algebraic system GAP(Groups, Algorithms and Programming). The main purpose is to motivate beginner students in this algebraic theory, and also to show the playful applicability to advanced students., [ES] En el presente trabajo mostramos cómo modelizar y analizar la resolubilidad de algunos puzzles, rompecabezas y juegos matemáticos, haciendo uso de conceptos básicos de la teoría de grupos y del sistema algebraico computacional GAP (Groups, Algorithms and Programming). Se trata de motivar al alumnado que se inicia en esta teoría algebraica y al mismo tiempo mostrar su aplicabilidad de una forma lúdica para aquellos estudiantes ya iniciados en este campo.

[EN] The subject Algebraic Methods and their Applications of the Master in Mathematical Research is focused on showing the applicability that some abstract algebraic structures have in various scientific areas, in both pure mathematics and other more applied contexts of real life. One of the main troubles when learning these structures is their high degree of abstraction which difficults the understanding, specially for beginner students in this topic, as well as the lack of applicability they have been treated before, focusing only in the mathematical aspect. The method of using games in teaching is an innovative and effective tool known as “game-based learning”. This pedagogic tendency is used as a playful component in a concrete learning objective. In this direction, the present paper concerns about the mathematical modelling of different puzzles and brainteasers, as well as the analysis of their solubility, through algebraic techniques that have been used in the aforementioned subject. The goal is to address the study of both the structure of a group and also its most basic properties. To do this, we make use in the classroom of the computational algebraic system GAP (Groups, Algorithms and Programming), which eases the computations in discrete algebra and which helps in a better understunding of this abstract structure. The case of the Rubik’s cube, one of the most celebrated and best-selling games in the world, and its variations are specially considered, [ES] La asignatura Métodos Algebraicos y sus Aplicaciones del Máster en Investigación Matemática está orientada a mostrar la aplicabilidad que ofrecen algunas estructuras algebraicas abstractas en diversas áreas científicas, tanto en la propia matemática pura como en otras áreas más aplicadas de nuestro entorno real. Uno de los principales problemas en el aprendizaje de dichas estructuras es su alto grado de abstracción que dificulta su entendimiento, principalmente para alumnos que se inician por primera vez en este campo, y la falta de aplicabilidad con las que han sido tratadas con anterioridad, centrándose en su aspecto puramente matemático.El método de utilizar juegos en la enseñanza es una innovadora y eficaz herramienta conocida como “game-based learning”. Esta tendencia pedagógica es utilizada como componente lúdica con un objetivo concreto de aprendizaje. En esta línea, la presente comunicación trata sobre la modelización matemática de diversos puzzles y rompecabezas, así como el estudio de su resolubilidad, mediante técnicas algebraicas que han sido utilizadas en la citada asignatura para abordar el estudio de la estructura de grupo y el análisis de sus propiedades más básicas. Para ello, hacemos uso en el aula del sistema algebraico computacional GAP (Groups, Algorithms and Programming), el cual facilita los cálculos en álgebra discreta y posibilita una mejor comprensión de esta estructura. El caso del cubo de Rubik, uno de los juegos más célebres y vendidos en el mundo, y sus variantes son considerados especialmente.

[EN] In this paper we show how to model and to analyse the solubility of some puzzles, brainteasers and other mathematical toys. We make use of basic group theory concepts and the computational algebraic system GAP(Groups, Algorithms and Programming). The main purpose is to motivate beginner students in this algebraic theory, and also to show the playful applicability to advanced students., [ES] En el presente trabajo mostramos cómo modelizar y analizar la resolubilidad de algunos puzzles, rompecabezas y juegos matemáticos, haciendo uso de conceptos básicos de la teoría de grupos y del sistema algebraico computacional GAP (Groups, Algorithms and Programming). Se trata de motivar al alumnado que se inicia en esta teoría algebraica y al mismo tiempo mostrar su aplicabilidad de una forma lúdica para aquellos estudiantes ya iniciados en este campo.

[EN] In this paper we show how to model and to analyse the solubility of some puzzles, brainteasers and other mathematical toys. We make use of basic group theory concepts and the computational algebraic system GAP(Groups, Algorithms and Programming). The main purpose is to motivate beginner students in this algebraic theory, and also to show the playful applicability to advanced students., [ES] En el presente trabajo mostramos cómo modelizar y analizar la resolubilidad de algunos puzzles, rompecabezas y juegos matemáticos, haciendo uso de conceptos básicos de la teoría de grupos y del sistema algebraico computacional GAP (Groups, Algorithms and Programming). Se trata de motivar al alumnado que se inicia en esta teoría algebraica y al mismo tiempo mostrar su aplicabilidad de una forma lúdica para aquellos estudiantes ya iniciados en este campo.

[EN] In this paper we show how to model and to analyse the solubility of some puzzles, brainteasers and other mathematical toys. We make use of basic group theory concepts and the computational algebraic system GAP(Groups, Algorithms and Programming). The main purpose is to motivate beginner students in this algebraic theory, and also to show the playful applicability to advanced students., [ES] En el presente trabajo mostramos cómo modelizar y analizar la resolubilidad de algunos puzzles, rompecabezas y juegos matemáticos, haciendo uso de conceptos básicos de la teoría de grupos y del sistema algebraico computacional GAP (Groups, Algorithms and Programming). Se trata de motivar al alumnado que se inicia en esta teoría algebraica y al mismo tiempo mostrar su aplicabilidad de una forma lúdica para aquellos estudiantes ya iniciados en este campo.

[EN] The subject Algebraic Methods and their Applications of the Master in Mathematical Research is focused on showing the applicability that some abstract algebraic structures have in various scientific areas, in both pure mathematics and other more applied contexts of real life. One of the main troubles when learning these structures is their high degree of abstraction which difficults the understanding, specially for beginner students in this topic, as well as the lack of applicability they have been treated before, focusing only in the mathematical aspect. The method of using games in teaching is an innovative and effective tool known as “game-based learning”. This pedagogic tendency is used as a playful component in a concrete learning objective. In this direction, the present paper concerns about the mathematical modelling of different puzzles and brainteasers, as well as the analysis of their solubility, through algebraic techniques that have been used in the aforementioned subject. The goal is to address the study of both the structure of a group and also its most basic properties. To do this, we make use in the classroom of the computational algebraic system GAP (Groups, Algorithms and Programming), which eases the computations in discrete algebra and which helps in a better understunding of this abstract structure. The case of the Rubik’s cube, one of the most celebrated and best-selling games in the world, and its variations are specially considered, [ES] La asignatura Métodos Algebraicos y sus Aplicaciones del Máster en Investigación Matemática está orientada a mostrar la aplicabilidad que ofrecen algunas estructuras algebraicas abstractas en diversas áreas científicas, tanto en la propia matemática pura como en otras áreas más aplicadas de nuestro entorno real. Uno de los principales problemas en el aprendizaje de dichas estructuras es su alto grado de abstracción que dificulta su entendimiento, principalmente para alumnos que se inician por primera vez en este campo, y la falta de aplicabilidad con las que han sido tratadas con anterioridad, centrándose en su aspecto puramente matemático.El método de utilizar juegos en la enseñanza es una innovadora y eficaz herramienta conocida como “game-based learning”. Esta tendencia pedagógica es utilizada como componente lúdica con un objetivo concreto de aprendizaje. En esta línea, la presente comunicación trata sobre la modelización matemática de diversos puzzles y rompecabezas, así como el estudio de su resolubilidad, mediante técnicas algebraicas que han sido utilizadas en la citada asignatura para abordar el estudio de la estructura de grupo y el análisis de sus propiedades más básicas. Para ello, hacemos uso en el aula del sistema algebraico computacional GAP (Groups, Algorithms and Programming), el cual facilita los cálculos en álgebra discreta y posibilita una mejor comprensión de esta estructura. El caso del cubo de Rubik, uno de los juegos más célebres y vendidos en el mundo, y sus variantes son considerados especialmente.

[EN] The subject Algebraic Methods and their Applications of the Master in Mathematical Research is focused on showing the applicability that some abstract algebraic structures have in various scientific areas, in both pure mathematics and other more applied contexts of real life. One of the main troubles when learning these structures is their high degree of abstraction which difficults the understanding, specially for beginner students in this topic, as well as the lack of applicability they have been treated before, focusing only in the mathematical aspect. The method of using games in teaching is an innovative and effective tool known as “game-based learning”. This pedagogic tendency is used as a playful component in a concrete learning objective. In this direction, the present paper concerns about the mathematical modelling of different puzzles and brainteasers, as well as the analysis of their solubility, through algebraic techniques that have been used in the aforementioned subject. The goal is to address the study of both the structure of a group and also its most basic properties. To do this, we make use in the classroom of the computational algebraic system GAP (Groups, Algorithms and Programming), which eases the computations in discrete algebra and which helps in a better understunding of this abstract structure. The case of the Rubik’s cube, one of the most celebrated and best-selling games in the world, and its variations are specially considered, [ES] La asignatura Métodos Algebraicos y sus Aplicaciones del Máster en Investigación Matemática está orientada a mostrar la aplicabilidad que ofrecen algunas estructuras algebraicas abstractas en diversas áreas científicas, tanto en la propia matemática pura como en otras áreas más aplicadas de nuestro entorno real. Uno de los principales problemas en el aprendizaje de dichas estructuras es su alto grado de abstracción que dificulta su entendimiento, principalmente para alumnos que se inician por primera vez en este campo, y la falta de aplicabilidad con las que han sido tratadas con anterioridad, centrándose en su aspecto puramente matemático.El método de utilizar juegos en la enseñanza es una innovadora y eficaz herramienta conocida como “game-based learning”. Esta tendencia pedagógica es utilizada como componente lúdica con un objetivo concreto de aprendizaje. En esta línea, la presente comunicación trata sobre la modelización matemática de diversos puzzles y rompecabezas, así como el estudio de su resolubilidad, mediante técnicas algebraicas que han sido utilizadas en la citada asignatura para abordar el estudio de la estructura de grupo y el análisis de sus propiedades más básicas. Para ello, hacemos uso en el aula del sistema algebraico computacional GAP (Groups, Algorithms and Programming), el cual facilita los cálculos en álgebra discreta y posibilita una mejor comprensión de esta estructura. El caso del cubo de Rubik, uno de los juegos más célebres y vendidos en el mundo, y sus variantes son considerados especialmente.

[EN] The subject Algebraic Methods and their Applications of the Master in Mathematical Research is focused on showing the applicability that some abstract algebraic structures have in various scientific areas, in both pure mathematics and other more applied contexts of real life. One of the main troubles when learning these structures is their high degree of abstraction which difficults the understanding, specially for beginner students in this topic, as well as the lack of applicability they have been treated before, focusing only in the mathematical aspect. The method of using games in teaching is an innovative and effective tool known as “game-based learning”. This pedagogic tendency is used as a playful component in a concrete learning objective. In this direction, the present paper concerns about the mathematical modelling of different puzzles and brainteasers, as well as the analysis of their solubility, through algebraic techniques that have been used in the aforementioned subject. The goal is to address the study of both the structure of a group and also its most basic properties. To do this, we make use in the classroom of the computational algebraic system GAP (Groups, Algorithms and Programming), which eases the computations in discrete algebra and which helps in a better understunding of this abstract structure. The case of the Rubik’s cube, one of the most celebrated and best-selling games in the world, and its variations are specially considered, [ES] La asignatura Métodos Algebraicos y sus Aplicaciones del Máster en Investigación Matemática está orientada a mostrar la aplicabilidad que ofrecen algunas estructuras algebraicas abstractas en diversas áreas científicas, tanto en la propia matemática pura como en otras áreas más aplicadas de nuestro entorno real. Uno de los principales problemas en el aprendizaje de dichas estructuras es su alto grado de abstracción que dificulta su entendimiento, principalmente para alumnos que se inician por primera vez en este campo, y la falta de aplicabilidad con las que han sido tratadas con anterioridad, centrándose en su aspecto puramente matemático.El método de utilizar juegos en la enseñanza es una innovadora y eficaz herramienta conocida como “game-based learning”. Esta tendencia pedagógica es utilizada como componente lúdica con un objetivo concreto de aprendizaje. En esta línea, la presente comunicación trata sobre la modelización matemática de diversos puzzles y rompecabezas, así como el estudio de su resolubilidad, mediante técnicas algebraicas que han sido utilizadas en la citada asignatura para abordar el estudio de la estructura de grupo y el análisis de sus propiedades más básicas. Para ello, hacemos uso en el aula del sistema algebraico computacional GAP (Groups, Algorithms and Programming), el cual facilita los cálculos en álgebra discreta y posibilita una mejor comprensión de esta estructura. El caso del cubo de Rubik, uno de los juegos más célebres y vendidos en el mundo, y sus variantes son considerados especialmente.