One hundred logicians make one hundred statements about themselves. Only one can survive scrutiny.
The Hundred Numbered Logicians
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?