Liars!

Logic Level 4

There are 100 people on an island; some people always tell the truth, and the others always lie.

A visitor asks them, "How many of you tell the truth?"

For \(n=1, 2, ..., 100,\) the \(n^\text{th}\) person replies, "\(f(n)\) of us tell the truth," where \(f(n)\) is the last two digits of \(n^2.\)

How many of them always tell the truth?

Note: All 100 islanders replied. For example, the \(3^\text{rd}\) person replied, "9 of us tell the truth" because \(3^2={\color{red}09}.\) and the \(17^\text{th}\) person replied, "89 of us tell the truth" because \(17^2=2{\color{red}89}.\)

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