If there are exactly 3 enthusiastic inhabitants, the person who said 4 must be enthusiastic along with those to their right, leading to 9 enthusiastic — contradiction!
Hypothetically, if there were 4 enthusiastic inhabitants, then logically at least 8 must be enthusiastic, which is again a contradiction due to answered numbers.
The key insight is that the answers given by half-hearted individuals cannot exceed the true number of enthusiasts, while enthusiastic answers must meet or exceed it.
Through elimination of the incorrect assumptions, the solution reveals that there are 6 enthusiastic inhabitants who have correctly assessed their group.
#math-puzzles #logical-reasoning #hungarian-mathematicians #problem-solving #enthusiasm-vs-half-heartedness
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