Solution
The Alternator Speaks Thrice
Show the problem again
Every inhabitant of an island is of exactly one of four kinds: a knight (every statement true), a knave (every statement false), a true-first alternator (statements alternate true, false, true, ...) or a false-first alternator (false, true, false, ...). A stranger makes three statements in this order: 1. "I am not a knave." 2. "I am an alternator." 3. "My first statement was true." What kind of inhabitant is the stranger? Answer with one of: knight, knave, alternator.
Worked solution
Test each kind against the required truth pattern of its three statements. A knight would need statement 2 to be true, but a knight is not an alternator. A true-first alternator needs statement 2 false, yet the stranger would be an alternator, making it true. A false-first alternator needs statement 1 false, yet being a non-knave makes it true. A knave must make all three false: he is a knave, so "I am not a knave" is false; he is not an alternator, so statement 2 is false; and his first statement was false, so statement 3 is false. Only the knave survives, as enumeration of the four kinds confirms. Answer: knave.
Source: Original puzzle; alternators are a standard extension of Smullyan's knights and knaves. Statement written for AxiomIQ.