DAIHINMIN, which means Grand Pauper, is a popular playing-card game in Japan. TANHINMIN is a simplified variant of DAIHINMIN, which was proposed by Nishino in 2007 in order to investigate the mathematical properties of DAIHINMIN. In this paper, we consider a 2-player generalized TANHINMIN, where the deck size is arbitrary n. We present a linear-time algorithm that determines which player has a winning strategy after all cards are distributed to the players.

The Voronoi game is a two-person perfect information game modeling a competitive facility location. The original version of the game is played on a continuous domain. Only two special cases (1-dimensional case and 1-round case) have been extensively investigated. Recently, the discrete Voronoi game of which the game arena is given as a graph was introduced. In this note, we give a complete analysis of the discrete Voronoi game on a path. There are drawing strategies for both the first and the second players, except for some trivial cases.

Generalized Tsume-Shogi (GTS) is Tsume-Shogi on the board of size n n for arbitrary n. The problem to decide the existence of a winning sequence of moves (where the attacker must always check) on an instance of GTS was proved to be exptime-complete by Yokota et al. (2000). This paper considers the complexity of yozume problem of GTS, which is, roughly speaking, the problem whether a given position of GTS has a winning sequence other than given sequences (though the actual rule of yozume is more complicated). The detection of yozume is an important issue in designing Tsume-Shogi problems, since the modern designing rule strongly prohibits it. We define a function problem of GTS appropriately to formulate yozume problem as its Another Solution Problem (ASP; the problem to decide the existence of solutions other than given ones). Moreover, we extend the existing framework for investigating ASPs so that it can be applied to exptime-complete problems. In particular, since the decision of correctness of given winning sequences is not easy, we establish a framework to treat ASP of function problems with promises. On the basis of these results, we prove that the decision version of yozume problem of GTS is exptime-complete as a promise problem using the existing reduction which was constructed by Yokota et al. to prove the exptime-completeness of GTS.