$5 \cdot 77$ The team leader assigns 9 or 10 people from 33 team members to duty every night. How many days at least are needed so that each member has the same number of duty shifts?
［Solution］Suppose 9 people are on duty for $k$ days, and 10 people are on duty for $n$ days, then each member is on duty for $m$ days. Thus, we have
$$
9 k+10 n=33 m \text {. }
$$

When $m=1$, the above equation has no positive integer solutions. When $m=2$, we get the unique solution: $\square$
$k=4, n=3$. The duty roster for these 7 days can be arranged as shown in the table on the right. The first 3 days each have 10 people on duty, and the last 4 days each have 9 people on duty, with each person on duty exactly twice over the 7 days. Therefore, it is known that it takes at least 7 days to ensure that each member is on duty an equal number of times.