A Round Table Conference

8 people have to be seated at a round banquet table. The seats are number 1-8. 

For this teaser, 5 is opposite 1, 6 is opposite 2 and so on. Likewise, "next to" means one of the neighboring seats only. i.e., 8 is next to 1 and 7.
A and H are the only French speaking people on the table. They need to be seated together. 

B and F should sit opposite each other. 

C, F, and G all know Russian, but don't necessarily need to sit next to each other. In fact, G wants to sit next to someone who knows French. 

D is English and insists on sitting next to at least one other English speaking person, and pat opposite the good looking H. E is the only other English speaker in the group, but he wants to sit next to someone who knows Russian. 

G agrees to sit next to F only on condition that the other side must have a French speaker. C does not sit next to either of them. 

C however, agrees to sit next to B, who is the only Bavarian in the group.
A will not sit next to a Russian or an English speaker.

THIS should be the seating arrangement! 

Seating Arrangement in A Round Table Conference

What was the arrangement challenge?

Given Data : 

8 people have to be seated at a round banquet table. The seats are number 1-8.

1. A and H are the only French speaking people on the table. They need to be seated together. 

2. B and F should sit opposite each other. 

3. C, F, and G all know Russian, but don't necessarily need to sit next to each other. In fact, G wants to sit next to someone who knows French. 

4. D is English and insists on sitting next to at least one other English speaking person, and pat opposite the good looking H. 

5. E is the only other English speaker in the group, but he wants to sit next to someone who knows Russian. 

6. G agrees to sit next to F only on condition that the other side must have a French speaker. C does not sit next to either of them. 

7. C however, agrees to sit next to B, who is the only Bavarian in the group.
A will not sit next to a Russian or an English speaker.

Arranging STEPS :

1] From (1) & (3), it's clear that G should be seating next to the A or H. That is G, A and H are occupying adjacent seats whose order is yet to be known. 

2] Now as per (2), B and F must be on opposite seats, they need to 'surround' the group of G - A - H. That's the only way they would be opposite. (There are 2 ways that they can do this and this would result into 2 possible solutions as concluded in conclusion).

3]  As per (6), G is ready to sit next to F so that G and F should be occupying adjacent seats. Order of seat to be occupied by A and H are yet to be known.

4] As per (7), C can seat next to B. A can't seat next to Russian G. 

5] As per (4) and (5), D & E should be next to each other but as per (4) D has to be opposite to H. 

CONCLUSION : 

In order to make seat arrangement in accordance with everyone's preference, we just need to ask them to seat in alphabetical order of their names. Here, seat number doesn't matter and what matters is that everyone is getting their favorite seat.

Interestingly, they can seat in circle clockwise or anticlockwise according to alphabetical order of their names.

 

Language Barrier in International Meeting

Of the 1985 people attending an international meeting, no one speaks more than five languages, and in any subset of three attendees, at least two speak a common language. Prove that some language is spoken by at least 200 of the attendees.

Here is the proof! 

For The Communication in International Meeting

What was the barrier in the communication?

For any attendee A and B, having no common language there must be C who know the language of either A or B to form a trio as mentioned.

Let's make assumption contradicting the statement made in question. Suppose there are only 198 people who can talk in particular language with A or B. Since A can communicate in 5 languages, there are 5 x 198 = 990 people who can talk with A.

That is 990 people are there who have sharing 1 common language with 1 of 5 languages known by A. Similarly, B also can communicate with 990 more people.

Now, if A and B have no common language then there are only 990 + 990 = 1980 people having potential to become C in the trio. This obviously doesn't cover total of remaining people i.e. 1985 - 2 (A and B) = 1983.

Hence, our assumption goes wrong there. So there must be at least 200 attendees knowing the same language .