5.9 The International Mathematical Olympiad Problem Selection Committee has 34 countries participating, with each country being represented by a team leader and a deputy leader. Before the meeting, the participants shake hands with each other, but the team leader and deputy leader from the same country do not shake hands. After the meeting, the team leader of the host country asks the participants how many times they shook hands, and the answers received are all different. How many people did the deputy leader of the host country shake hands with?
[Solution] Clearly, each person can shake hands with at most 66 people. Since the answers of 67 people are all different, the set of answers is of course $\{0,1, \cdots, 66\}=E$. For each $k \in E$, there is exactly one person $p(k)$ who has shaken hands with exactly $k$ people.
$p(66)$ shakes hands once with each of the 66 people from the other 33 countries, so each of the other 66 people has shaken hands at least once, which means $p(0)$ must be from the same country as $p(66)$, and they are certainly not the leader and deputy leader of the host country. The only person who shook hands with $p(1)$ is, of course, $p(66)$. Therefore, $p(0)$ and $p(1)$ are the only two people who did not shake hands with $p(65)$, so $p(1)$ and $p(65)$ must be from the same country. Similarly, it can be known that $p(j)$ and $p(66-j)$ are from the same country, $j=2$, $3, \cdots, 32$. Therefore, the deputy leader of the host country is $p(33)$, who has shaken hands with exactly 33 people.