"Matlab解夫妻过河问题多步决策数学模型研究"

The problem of couples crossing the river has been a challenging logical puzzle since the 8th century, with many mathematical modeling textbooks addressing it. The problem involves different objects or organisms, some of which cannot coexist, gradually crossing a river in small groups from one bank to the other. After a finite number of steps, all members of the group must reach the other bank without any losses. In the context of the couples crossing the river problem, we find that the problem of state transitions may not always have a solution, and even when there is a solution, it may not follow a specific pattern. This paper uses graphical and Matlab programming methods to solve the problem of whether 5 or 6 pairs of couples can safely cross the river, and extends the analysis to n pairs of couples and m pairs of boats for determining the relationship between them in order to safely cross the river. The key words in this study are multi-step decision making, Matlab, mathematical modeling, and the problem of crossing the river.