Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 12J / c / Solution

If an automaton with at most $100$ states accepted a word $w\in L$ of length $100$, the preceding loop argument would produce $x{y}^{i}z\in L$ for every $i\ge 0$, with $y\ne \epsilon$. These words have unbounded lengths and are distinct, contradicting the finiteness of $L$.