13. $A, B, C$ three people go to the library to read books regularly, where $A$ goes every 1 day, $B$ goes every 2 days, and $C$ goes every 3 days. On the last day of February, the three meet at the library. From March 1st to June 30th, there are days when only 1 person comes to the library. $\qquad$
Analysis: The test point is the principle of inclusion and exclusion.
This type of question requires students to master the specific content of the principle of inclusion and exclusion, as well as the ability to apply it to solve practical problems.

The first method: Using the principle of inclusion and exclusion.
$A$ goes every 1 day, which means every 2 days, or the time of each visit is a multiple of 2 days;
$B$ goes every 2 days, which means the time of each visit is a multiple of 3 days;
$C$ goes every 3 days, which means the time of each visit is a multiple of 4 days;
The requirement is to find how many days from March 1 to June 30 only one person visits the library, which is essentially to find how many days there are without overlapping visits.
It can be concluded that a total of 122 days have passed.
First case: Calculate the days when only $B$ visits, $[122 \div 3]=40$ days, $A B$ visit simultaneously: $[122 \div (3 \times 2)]=20$ then the days when only $B$ visits are $40-20=20$ days.
Second case: Calculate the days when only $A$ visits, $[122 \div 2]=61$ days, $A B$ visit simultaneously: $[122 \div (3 \times 2)]=20, A C$ visit simultaneously: $120 \div 4=30$ days, visit simultaneously: $[122 \div (3 \times 4)]=10$ days
Then the days when only $A$ visits are $61-20-30+10=21$ days.
Thus, the days when only one person visits are $20+21=41$ days.
The second method: Using the cycle: They visit every 2 days, every 3 days, and every 4 days, so every 12 days is a cycle,
So it can be determined from the chart that, in these 12 days, the number of days when only one person visits the library is 4 days,
$$
122 \div 12=10 \text { (groups) } \cdots \cdots \cdot 2 \text { (days) }
$$

So there are a total of $4 \times 10+1=41$ (days)