11-2. At a round table, 14 conference participants were seated. During the break, some of them (but not all) went to have coffee. It turned out that each participant who remained at the table had exactly one neighbor who left. How many participants could have gone for coffee? Provide all possible answers.
Answer: 6, 8, 10, or 12 participants.

Solution. Let participant A remain at the table. Then, one of his neighbors, let's say B, also remained. But one of B's neighbors also remained, and it is participant A. Therefore, all the participants who remained at the table can be paired.

Thus, the remaining participants sit in pairs, and between the pairs, any number of participants (but no fewer than 1) went to drink coffee. This means that 2, 4, 8, 10, etc., participants remained. However, 10 or more could not have remained: between five or more pairs, there would be at least 5 participants who went to drink coffee, and the total would be no less than 15 people at the table, but according to the condition, there are 14.

Since 2, 4, 6, or 8 participants remained, then 6, 8, 10, or 12 participants went to drink coffee.