8.5 On an island, there live 25 people: knights, liars, and tricksters. Knights always tell the truth, liars always lie, and tricksters answer the questions posed to them in turn, alternating between truth and lies. All the islanders were asked three questions: "Are you a knight?", "Are you a trickster?", "Are you a liar?" (the questions were asked in the exact order specified). To the first question, 21 people answered affirmatively, to the second - 17 people, to the third - 6 people. How many knights live on this island?
Solution. Each knight will answer "yes" to the first question and "no" to the other two. Each liar will answer "yes" to the first two questions and "no" to the last one. The tricksters can be divided into those who answered the first question truthfully (tricksters of the first type) and those who answered the first question falsely (tricksters of the second type). Tricksters of the first type will answer "no" to all questions, while tricksters of the second type will answer "yes" to all questions. The results can be recorded in a table:

| Type of inhabitant | Are you a knight? | Are you a trickster? | Are you a liar? |
| :---: | :---: | :---: | :---: |
| Knight | yes | no | no |
| Liar | yes | yes | no |
| Trickster 1 type | no | no | no |
| Trickster 2 type | yes | yes | yes |
| Number of "yes" answers | 21 | 17 | 6 |

Note that only tricksters of the second type will answer affirmatively to the last question. Therefore, there are 6 tricksters of the second type. Only tricksters of the first type will not answer affirmatively to the first question, and there are $25-21=4$ of them. The second question will be answered affirmatively by liars and tricksters of the second type (and only them), so there are $17-6=11$ liars. Therefore, the number of knights on the island is $25-6-4-11=4$.

Answer: 4 knights.

| IS IN THE SOLUTION | SCORE |
| :--- | :---: |
| Correct and justified answer | 7 points |
| Correct approach with arithmetic errors, possibly leading to an incorrect answer | deduct 1 point for each error |
| Correctly and justifiedly found only the number of liars or only the number of tricksters | 3 points |
| Considering two types of tricksters (not leading to a solution) | 2 points |
| Correct answer without justification | 1 point |