The algebraic solvability of the novel lamplighter puzzle

In this study, the group of finite cyclic lamplighter states is reinterpreted as the novel lamplighter puzzle. The rules of the puzzle are outlined and related back to properties of the lamplighter group with specific interest placed upon the discussion of which puzzle instances are solvable. The paper shows that, through the use of algebra, many puzzle instances can be identified as solvable without the use of an exhaustive search algorithm. Solvability depends upon the creation of irregular generating sets for subgroups of the finite cyclic lamplighter group and the cosets formed by these subgroups. Further possible generalizations of the lamplighter puzzle are also discussed in closing.

Chess without draws

The prevalence of draws in chess is an increasing concern: in the ICCF’s 2017 ‘MT van Oosteram’ Correspondence event, all 56 games were drawn. This article reports a ‘Mobility Chess’ proposal by ‘Aloril’ which addresses this problem. He prefers to retain his anonymity but should be regarded as the primary author of this paper. He has defined a logical sequence of increasingly subtle and decreasingly rewarded ‘winning’ goals G k . Each position in itself associates with both an immediate achievement A j of goal G j – and an ultimate, best-achievable goal G k , k ⩽ j. Therefore, Aloril has eliminated the draw in Mobility Chess and shown how Chess can reduce the incidence of draws as much as required.

On the power of lookahead in single-player PuyoPuyo

PuyoPuyo is one of the Tetris-type games, which is dealt with as a single-player game in this paper. The player has a winning strategy if the player can keep playing the game infinitely on a gameboard of a constant height. In this paper, we consider how lookahead of input pieces affects the existence of winning strategies in PuyoPuyo, and show conditions that the player cannot win even with lookahead. First, we show the number of colors sufficient to make the player lose on the gameboard of width w when the number of lookahead pieces is m. Next, we show that ten and twenty-six colors are sufficient to make the player lose on the gameboards of width two and three, respectively, no matter how large the number of lookahead pieces is.

The Computer Olympiad 2020

The 23rd Computer Olympiad was held November/December 2020. As a consequence of the global pandemic, for the first time the competitions were fought online. This involved creating new rules that were, in large part, dependent on having the participants cooperate on organizing and conducting the events. The event was a success and will be repeated online in 2021.

An efficient AI-based method to play the Mahjong game with the knowledge and game-tree searching strategy

The Mahjong game has widely been acknowledged to be a difficult problem in the field of imperfect information games. Because of its unique characteristics of asymmetric, serialized and multi-player game information, conventional methods of dealing with perfect information games are difficult to be applied directly on the Mahjong game. Therefore, AI (artificial intelligence)-based studies to handle the Mahjong game become challenging. In this study, an efficient AI-based method to play the Mahjong game is proposed based on the knowledge and game-tree searching strategy. Technically, we simplify the Mahjong game framework from multi-player to single-player. Based on the above intuition, an improved search algorithm is proposed to explore the path of winning. Meanwhile, three node extension strategies are proposed based on heuristic information to improve the search efficiency. Then, an evaluation function is designed to calculate the optimal solution by combining the winning rate, score and risk value assessment. In addition, we combine knowledge and Monte Carlo simulation to construct an opponent model to predict hidden information and translate it into available relative probabilities. Finally, dozens of experiments are designed to prove the effectiveness of each algorithm module. It is also worthy to mention that, the first version of the proposed method, which is named as KF-TREE, has won the silver medal in the Mahjong tournament of 2019 Computer Olympiad.