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,n=1, 2, ..., 100, the nthn^\text{th} person replies, "f(n)f(n) of us tell the truth," where f(n)f(n) is the last two digits of n2.n^2.

How many of them always tell the truth?

Note: All 100 islanders replied. For example, the 3rd3^\text{rd} person replied, "9 of us tell the truth" because 32=09.3^2={\color{#D61F06}09}. and the 17th17^\text{th} person replied, "89 of us tell the truth" because 172=289.17^2=2{\color{#D61F06}89}.

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