Question

On an island inhabited by kings and peasants, where the former always tell the truth and the latter always lie, you meet three individuals: Erin, William, and Sam. Erin says that William is a king. William says that Erin is a king but Sam is a peasant. Sam says that both Erin and William are kings. Determine who is a king and who is a peasant by constructing a truth table.

Answer 1

Let

A - Erin

B - William

C - Sam

Let 1 represent a truth and 0 represent a lie. Then a king will be assigned the value 1 since a king always tells the truth and a peasant will be assigned a value 0 since a peasant always lies.

Then, let

a - What Erin said which is "B=1"

b - What William said which is "A=1 C=0"

c - What Sam said which is "A=1 B=1"

P - The situation where "A=a B=b C=c"

We need to find the situation where P=1 and thus P is true because if P is true, then a king will tell the truth and a peasant will tell a lie which is as per the question.

We construct the truth table as follows:

A	B	C	a	b	c	P
0	0	0	0	0	0	1
0	0	1	0	0	0	0
0	1	0	1	0	0	0
0	1	1	1	0	0	0
1	0	0	0	1	0	0
1	0	1	0	0	0	0
1	1	0	1	1	1	0
1	1	1	1	0	1	0

We can see from the truth table that P=1 only when A=0, B=0, C=0.

Since A, B and C are all 0, so everyone lies and thus everyone is a peasant.

Hence, Erin is a peasant, William is a peasant and Sam is a peasant.