Question

Another meeting

Answer 1

34 countries participated in a jury session of the Openstudy,
each represented by the leader and the deputy leader of the team. Before
the meeting, some participants exchanged handshakes, but no team leader
shook hands with his deputy. After the meeting, the leader of the American
team asked every other participant the number of people they had shaken
hands with, and all the answers she got were different. How many people
did the deputy leader of the American team greet?
you can substitute America for you own country...

Answer 2

i have no solution for this one

Answer 3

,

I'll explain this for a fewer number,
suppose that the meeting was held among 4 countries, since there are two from each country altogether there are 8 participants.

In the graph I've used A,B,C,D, for country leaders and A1,B1,... for their assistants.

The answering starts with the statement which says all 7 of the participants gives separate answers so they should be 6,5,4,3,2,1,0 (7 is not possible since one cannot shake hand with the partner or with himself).

Assume D1 has shaken hands with 6 of them, then automatically D cannot shake hands with any other (since there should be a person with 0 hand shakes)

Like wise assume C1 has shaken hands with 5 of them, then automatically C can shake hands with only 1 (that is D1)

Like wise we can get the number of hand shakes of all the participants

Eventually we see that two people get the equal amount of hand shakes (3 in this case). So one of them should be the person who asks the question and the other should be his deputy. So in this case the answer that the deputy gives is 3