Making Change in 2048

The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by proving a min-max theorem equating this maximum score (in an abstract generalized variation of 2048 that allows all the moves of the original game) with the minimum value that causes a greedy change-making algorithm to use a given number of coins. A widely-followed strategy in 2048 maintains tiles that represent the move number in binary notation, and a similar strategy in the Fibonacci number variant of the game (987) maintains the Zeckendorf representation of the move number as a sum of the fewest possible Fibonacci numbers; our analysis shows that the ability to follow these strategies is intimately connected with the fact that greedy change-making is optimal for binary and Fibonacci coinage. For variants of 2048 using tile values for which greedy change-making is suboptimal, it is the greedy strategy, not the optimal representation as sums of tile values, that controls the length of the game. In particular, the game will always terminate whenever the sequence of allowable tile values has arbitrarily large gaps between consecutive values

Languages of games and play: A systematic mapping study

Digital games are a powerful means for creating enticing, beautiful, educational, and often highly addictive interactive experiences that impact the lives of billions of players worldwide. We explore what informs the design and construction of good games to learn how to speed-up game development. In particular, we study to what extent languages, notations, patterns, and tools, can offer experts theoretical foundations, systematic techniques, and practical solutions they need to raise their productivity and improve the quality of games and play. Despite the growing number of publications on this topic there is currently no overview describing the state-of-the-art that relates research areas, goals, and applications. As a result, efforts and successes are often one-off, lessons learned go overlooked, language reuse remains minimal, and opportunities for collaboration and synergy are lost. We present a systematic map that identifies relevant publications and gives an overview of research areas and publication venues. In addition, we categorize research perspectives along common objectives, techniques, and approaches, illustrated by summaries of selected languages. Finally, we distill challenges and opportunities for future research and development

Feature Papers "Age-Friendly Cities & Communities: State of the Art and Future Perspectives"

The "Age-Friendly Cities & Communities: States of the Art and Future Perspectives" publication presents contemporary, innovative, and insightful narratives, debates, and frameworks based on an international collection of papers from scholars spanning the fields of gerontology, social sciences, architecture, computer science, and gerontechnology. This extensive collection of papers aims to move the narrative and debates forward in this interdisciplinary field of age-friendly cities and communities

Approaches and Methods of Science Teaching and Sustainable Development

This book “Approaches and Methods of Science Teaching and Sustainable Development”, edited by Dr. David González Gómez and Dr. Jin Su Jeong, aims to provide a solid research corpus for addressing the challenges needed to provide adequate science and sustainable development education to scholars with different levels of education. Sustainability is starting to form a part of the curricula for many educational institutions. However, efforts must be taken to ensure proper implementation and development of sustainability-oriented topics seeking the sustainable development goals (SDGs) in higher education as well as fresh perspectives on continuing challenges

Remote Sensing and Geosciences for Archaeology

This book collects more than 20 papers, written by renowned experts and scientists from across the globe, that showcase the state-of-the-art and forefront research in archaeological remote sensing and the use of geoscientific techniques to investigate archaeological records and cultural heritage. Very high resolution satellite images from optical and radar space-borne sensors, airborne multi-spectral images, ground penetrating radar, terrestrial laser scanning, 3D modelling, Geographyc Information Systems (GIS) are among the techniques used in the archaeological studies published in this book. The reader can learn how to use these instruments and sensors, also in combination, to investigate cultural landscapes, discover new sites, reconstruct paleo-landscapes, augment the knowledge of monuments, and assess the condition of heritage at risk. Case studies scattered across Europe, Asia and America are presented: from the World UNESCO World Heritage Site of Lines and Geoglyphs of Nasca and Palpa to heritage under threat in the Middle East and North Africa, from coastal heritage in the intertidal flats of the German North Sea to Early and Neolithic settlements in Thessaly. Beginners will learn robust research methodologies and take inspiration; mature scholars will for sure derive inputs for new research and applications