Propositiones ad Acuendos Juvenes/Problems/17 - De Tribus Fratribus Singulas Habentibus Sorores/Solution 1

Solution
The constraint here is that at no time may a man be on the same bank as (or in the boat with) the sister of another, without the brother of that sister being present as well.

Let $M_1$, $M_2$ and $M_3$ denote the men, and $S_1$, $S_2$ and $S_3$ denote their respective sisters.

Let them be crossing from $A$ to $B$.

As follows:
 * $M_1$ and $S_1$ cross from $A$ to $B$.


 * $M_1$ crosses back alone from $B$ to $A$.


 * $S_2$ and $S_3$ cross from $A$ to $B$.


 * $S_1$ crosses back alone from $B$ to $A$.


 * $M_2$ and $M_3$ cross from $A$ to $B$.


 * $M_2$ and $S_2$ cross back from $B$ to $A$.


 * $M_1$ and $M_2$ cross from $A$ to $B$.


 * $S_3$ crosses back alone from $B$ to $A$.


 * $S_1$ and $S_3$ cross from $A$ to $B$.


 * $M_3$ crosses back alone from $B$ to $A$.


 * $M_3$ and $S_3$ cross from $A$ to $B$.


 * "And that would complete the crossing without anything untoward happening."

This was the original solution given in by.

It is not optimal.