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 Hillside Shepherds (Posted on 2012-07-10)
In every group of shepherds in a certain island, at least one is a knight, who always speaks truthfully, and at least one is a liar, who always speaks falsely.

A visitor approached four shepherds (denoted by A, B, C and D) on a hillside and asked each how many of the four were knights. These answers were given:

A: Three of us are knights.
B: One of us is a knight.
C: Two of us are knights.
D: None of us is a knight.

The visitor approached four more shepherds on another hillside (denoted by E, F, G and H) and asked how many were liars. Their answers follow:

E: We are all liars.
F: One of us is a liar.
G: Three of us are liars.
Shepherd H declined to speak.

How many of the shepherds on each of the two hillsides were knights?

 No Solution Yet Submitted by K Sengupta Rating: 5.0000 (1 votes)

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 Easier than D3 Comment 3 of 3 |
Obviously, only one of A, B, C, and D can be a knight. Since there is at least one knight, there is exactly one knight out of A, B, C, and D. B said that there was one knight, so the knight is B.

In the second group, E has to be a liar. Also, either F or G is a liar. There cannot be only one liar, so F is a liar. Therefore, either G or H is a knight. If G is a liar, then H is a knight, but then G would be telling the truth. That means that G is a knight, so H is a liar. Therefore, there is one knight out of E, F, G, and H. The knight is G.

The numbers of knights are 1 and 1.

 Posted by Math Man on 2012-07-12 11:47:59

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