- Knight: (produced by KK homozygous and KO heterozygous genotypes),
- Liar: (produced by LL homozygous and LO heterozygous genotypes),
- Knave: (produced by the KL heterozygous genotype), and
- Transposer: (produced by the OO homozygous genotype).
Knights always tell the truth, liars always lie, knaves' statements strictly alternate between truth and lie, and a transposer's statements are always of opposite truth-value to the person who spoke immediately before. (If a transposer is the first to make a statement, he or she will randomly choose between telling the truth or lying for their first statement.
Given the following statements from Zander, Yvette, Xerxes, and Willow, can you determine the genotype of each Kivelian, as well who is related to whom?
Willow: Exactly three of us are homozygous.
Zander: I have an L allele.
Xerxes: I am homozygous.
Yvette: I am a knight.
Zander: I am a knight.
Yvette: One of us is not directly related to the other three.
Willow: I am heterozygous.
Xerxes: I am a transposer.
Yvette: Two of us share the same genotype, and I'm not one of them.
Xerxes: I have a K allele.
Zander: I am homozygous.
Willow: Yvette is heterozygous.
Xerxes: Willow is heterozygous.
Willow: Xerxes is heterozygous.
Yvette: Between the four of us, we have exactly two K alleles.
Zander: At least one of us is a knave.
Note: The spacing used is only for readability; you may assume all statements were said consecutively in the order shown.