1. On the island of knights and liars (liars always lie, knights always tell the truth), each resident supports exactly one football team. In a survey, all residents of the island participated. To the question "Do you support 'Rostov'?", 40% of the residents answered "Yes". To a similar question about 'Zенit', 30% answered affirmatively, about 'Locomotive' - 50%, and about CSKA - 0%. What percentage of the island's residents actually support 'Rostov'?
Solution. Let $x \%$ of the island's inhabitants be liars. Then $(100-x) \%$ are knights. Since each knight answered affirmatively to exactly one of the questions, and each liar to three, we have $(100-x)+3 x=40+30+50$, from which $x=10$. Since none of the island's inhabitants said they support CSKA, all liars support CSKA. Each of them claimed to support "Rostov," so the actual supporters of "Rostov" are $40 \% - 10 \% = 30 \%$ of the population. Answer: $30 \%$.