Too many trolls

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This is a logic puzzle I made up for UNC's Math Challenge Problem

Puzzle

While walking through a fictional forest, you come upon a large group of trolls. The trolls all look identical, but you know that some of the trolls are knights who always tell the truth, while the rest of the trolls are knaves who always lie. Each troll makes a single statement.

The first troll says, "Hi, I'm Tucker."

The remaining 41 trolls each say, in order, "If the previous troll is a knight, then by the time I'm done speaking you will have heard more lies that truths."

Is the first troll's name really Tucker? And which of the remaining trolls are knight and which are knaves?

Help

Hint
Answer
Solution

See also