# 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 $3^2={\color{#D61F06}09}.$ and the $17^\text{th}$ person replied, "89 of us tell the truth" because $17^2=2{\color{#D61F06}89}.$

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