5.52 One day, three boys, Jia, Yi, and Bing, met at the library. Jia said, “From now on, I will come to the library every other day.” Yi said he would come every two days, and Bing said he would come every three days. After hearing their conversation, the librarian pointed out that the library is closed every Wednesday. The children replied that if any of them was supposed to come on a day when the library was closed, they would come the next day instead, and their subsequent visits to the library would be based on this new day. The children all followed this rule. One day, they met again at the library, and it was a Monday. On which day of the week did the above conversation take place?
[Sol] We start from Monday and count backward, listing the days they each came to the hall. We stop when we encounter Wednesday, but when we encounter Thursday, we must consider both possibilities and not ignore either. The specific listings are as follows:
甲: $\left\{\begin{array}{l}1,6,4,2,7,5 ; \\ 1,6,4,1,6,4, \cdots .\end{array}\right.$
乙: $1,5,2,6$.
丙: $\left\{\begin{array}{l}1,4,7 ; \\ 1,4,6,2,5,1, \cdots\end{array}\right.$

It is easy to see that the day the three people talked is 9 days ago, which was a Saturday.