One hundred logicians make one hundred statements about themselves. Only one can survive scrutiny.

The Hundred Numbered Logicians

Reasoner
Pure logic

Riddle statement

In a room there are one hundred logicians.

The first one says:
“There is exactly 1 liar here.”

The second one says:
“There are exactly 2 liars here.”

The third says:
“There are exactly 3 liars here.”

And so on, until the last one, who says:
“There are exactly 100 liars here.”

Every logician is either a truth-teller, who always tells the truth, or a liar, who always lies.

How many truth-tellers are there?