*Five, (20 points) 100 matchboxes, numbered 1 to 100. We can ask whether the total number of matches in any 15 boxes is odd or even. What is the minimum number of questions needed to determine the parity (odd or even) of the number of matches in box 1?
Let $a_{i}$ represent the number of matches in the $i$-th box.
The first time, boxes 1 to 15 are taken, so the parity of $\sum_{k=1}^{15} a_{k}$ is known;

The second time, boxes 2 to 8 and 16 to 23 are taken, so the parity of $\sum_{k=2}^{8} a_{k}+\sum_{k=16}^{23} a_{k}$ is known;

The third time, boxes 9 to 23 are taken, so the parity of $\sum_{k=9}^{23} a_{k}$ is known. From the three parities, it is easy to determine the parity of $a_{1}+2 \cdot \sum_{k=2}^{23} a_{k}$. If it is odd, then $a_{1}$ is odd; otherwise, $a_{1}$ is even.
Clearly, asking only once is not enough. Asking only twice is also not enough.
It is easy to see that in the two questions, $a_{1}$ must be included exactly once. Suppose $a_{1}$ and $a_{2}$ are included in the first question. We then consider two cases:
(1) If $a_{2}$ is not included in the second question, then changing the parity of both $a_{1}$ and $a_{2}$ simultaneously does not affect the answer, so the parity of $a_{1}$ cannot be determined.
(2) If $a_{2}$ is included in the second question, since $a_{1}$ is not included in the second question, the second question must include some $a_{3}$, which does not appear in the first question. Then, changing the parity of $a_{1}$, $a_{2}$, and $a_{3}$ simultaneously does not affect the answer, so the parity of $a_{1}$ cannot be determined.
In summary, at least three questions are required.