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Hillside Shepherds (Posted on 2012-07-10) Difficulty: 3 of 5
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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Solution Easy as A, B, C, D (spoiler) | Comment 1 of 3
In each group, all knights would give the same answer.  

In the first group, as all answers are different, there is exactly one knight.

In the 2nd group, we have three different answers and one who declined to speak.  This means that there are one or two knights, and therefore 2 or 3 liars.  Therefore,  E is a liar and F is a liar.  If G was also a liar, then that would make H the only knight, but that would lead to a contradiction because G's statement is then true.  Therefore, G is a knight, which means that H (based on G's statement) is a liar.

So there is only one knight in each group (B and G). 

Edited on July 11, 2012, 1:24 am
  Posted by Steve Herman on 2012-07-10 13:36:22

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