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| Knights, Liars, and Spies II (Posted on 2022-02-18) |
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We refer to the remote, mysterious island in the earlier problem, with Knights, who always tell the truth; Liars, who always lie; and Spies who speaks truthfully or falsely at will.
Marty, who was visiting this island, was approached by three men. One wears blue, one wears red and one wears green. Marty knows one is a knight, one is a liar and the remaining person, a spy. However, he is ignorant of the precise type of each of the three individuals.
Marty asks them their types, and they respond as follows:
o The man in blue says, "I am not a spy."
o The man in red says, "I am a liar."
o The man in green says, "If you asked me, I would say that the man in red is the spy."
Determine the precise types of the three men.
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Submitted by K Sengupta
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Rating: 4.0000 (1 votes)
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Solution:
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(Hide)
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The man in blue is the knight.
The man in red is the spy.
The man in green is the liar.
EXPLANATION:
Assume that the man in red is the liar. Then, we observe that he has spoken truthfully. This is a contradiction.
Assume that the man in red is the knight.
Then, he has falsely identified himself as a liar. Contradiction.
Accordingly, it follows that the man in red must be the spy who has chosen to speak falsely.
Hence, the remaining two men must be the knight and the liar, although not necessarily in this order.
Assume that the man in blue is the liar. Then, we observe that he has spoken truthfully, which is a contradiction.
Accordingly, the man in blue must be the knight who truthfully states that he is not a spy.
Then, the remaining person, that is, the man in green must be the liar.
Although the man in red is the spy but according to the man in green's statement his (green) intention is untrue and he would definitely lie if Marty really asked him that question about the man in red's identity. So, the man in green's statement is consistent with his type.
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Subject |
Author |
Date |
 | Solution | Kenny M | 2022-02-18 09:28:41 |
| Solution? | tomarken | 2022-02-18 07:08:39 |
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