"Matlab解决夫妻过河问题：多步决策与数学模型研究"

The problem of couples across the river has been a challenging logical puzzle since the 8th century. It involves different objects or living beings, some of which cannot coexist with each other, gradually crossing from one side of the river to the other. After a finite number of steps, the entire group must reach the opposite bank without any losses. The solution to this problem is not always straightforward and may not follow a consistent pattern. In this undergraduate thesis titled "Matlab Solution to the Problem of Couples Across the River," the problem is explored using graph theory and Matlab programming to determine if 5 or 6 pairs of couples can safely cross the river. The study is then extended to consider the relationship between n pairs of couples and the capacity of the boat to determine if they can cross the river safely. This research focuses on multi-step decision-making, mathematical modeling, and the analysis of the crossing problem using Matlab. Key words: multi-step decision-making, Matlab, mathematical modeling, crossing problem.