December 2022
Problem of the Month
The Island People
Submitted by K. Sengupta
A distant island has four types of people.
The first type are the Truthtellers, who always tell the truth.
The second type are the Liars, who always lie.
The third type are the Alternators, who strictly alternate between telling the truth and a lie, or, vice-versa.
The fourth type are the Doubloons.
A Doubloon is a type similar to an Alternator, except that a Doubloon's truth pattern is precisely two true statements
followed by two false statements or, two false statements followed by two true statements.
Aaron, Beau and Chuck are inhabitants of this island.
It is known that the three individuals belong to three different types.
They make these statements:
AARON
1. I am a Truthteller.
2. Beau is a Doubloon.
3. Chuck is the Alternator.
BEAU
1. I am the Alternator.
2. Chuck is the Doubloon.
3. Aaron is the Liar.
CHUCK
1. I am a Liar.
2. Aaron is the Doubloon.
3. Beau is the Truthteller.
Determine the types corresponding to each of these three individuals.