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Saturday, September 5, 2015
Island X
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There are three categories of tribes in Island X; a Truther, who
always speaks truthfully; a Liar, who always speaks falsely; and an
Altetnator, who makes statements that are alternatively truthful and
false, albeit not necessarily in that order.
A visitor approaches three inhabitants and asks who is a Truther. They answer as follows:
A says:
1. I am a Truther
2. B is a Liar
B says:
1. I am a Alternator
2. C is a Liar
C says:
1. I am a Truther
2. A is a Liar
Determine the identity of each of the three inhabitants from the information provided in the above statements.
A visitor approaches three inhabitants and asks who is a Truther. They answer as follows:
A says:
1. I am a Truther
2. B is a Liar
B says:
1. I am a Alternator
2. C is a Liar
C says:
1. I am a Truther
2. A is a Liar
Determine the identity of each of the three inhabitants from the information provided in the above statements.
Island X Puzzle Solution
Assume that A is the Truther. If so, then B is the Liar as A's statement asserts. If so, B's second statement is false, so C is the Alternator. This implies that C's first statement is false as also his second statement that A is the Liar, so that C is the Liar which is a contradiction, so that A cannot be the Truther.Assume that B is the Truther. If so, his first statement is a direct contradiction, implying amongst other things, that B cannot be the Truther.
Assume that C is the Truther. If so, then A is the Liar in conformity with his second statement, so the remaining member B must be the Alternator. This checks out since as a Alternator, B's first statement is true while in his second statement he falsely identified C as the Liar. Both of A's statement are then clearly false, so this establishes the veracity of both the statements of C.
Consequently, (A, B, C) = (Liar, Alternator, Truther)
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