We discuss puzzles of prisoners and hats with infinitely many prisoners and more than two hat colors. Assuming that the set of hat colors is equipped with a commutative group structure, we prove strategic equivalence among puzzles of several protocols with countably many prisoners.

This paper studies the theory and practice of Minna in Manabi, as the Japanese concept of learning from the perspective of moral education. The Japanese word Minna, which means “all” or “everyone,” plays an important role in Manabi. The word “Minna” is often found in textbooks used in moral education classes, and great value is placed on “thinking about everyone.” Minna, a component of Manabi, not only makes the self (the learner) nothing and selfless, but also makes it possible to (...) enter all, everyone, and the world. This may create possibilities for inclusiveness, reciprocal harmony, hospitality, solidarity, and cooperativeness. This Manabi of “thinking about everyone” can be found in moral classes and in all aspects of learning (educational) activities in Japanese schools. Among them, in addition to being a traditional Buddhist practice dealing with Nothingness and Selflessness, Souji (cleaning time) is also very important in schools as a Japanese moral practice of “thinking about everyone.” The moral concepts developed in the West, such as democracy, community, solidarity, engagement, and citizenship, are not only realized through the establishment of the individual, self-realization, and perfection of personality, but by “thinking about everyone,” as expressed in Nothingness, Selflessness, and Minna. (shrink)