Heather is engaged to either Abe, Brad, Cody, or Dean. Each of the four men plus Heather is either a Knight, who always tells the truth or a Liar, who always speaks falsely.
Their statements are as follows:
- Abe says, "Exactly one of us four men always tells the truth".
- Brad says, "Exactly one of us four men always lies".
- Cody says, "Heather's fiancé is either Abe or Brad."
- Heather says, "My fiancé and I either always tell the truth or always lie".
Who is Heather's fiancé? What are the types of the five individuals?
I reached the same conclusion as Charlie, but with much more stream-of-consiousness verbosity.
My conclusion:
Abe is the sole male Liar, with Brad, Cody, and Dean being Knights.
Brad is the fiancé.
It can not be determined whether Heather, who is the fiancée, is Knight or Liar.
From Heather's statement:
The fiancé is a Knight.
Heather could be either Knight or Liar.
The male Knights number either zero or more than one.
Assume Abe is Knight: then B,C,D are Liars. A, the sole Knight must be the fiancé. But from C, fiancé is C or D. Since this is a contradiction, A must be a Liar and the men consist of either zero or more than one Knights.
We now know A is Liar.
Assume Brad is Knight: A is the sole male Liar. From C, the fiancé is A or B, but since A is Liar and we're assuming B is Knight B must be the fiancé.
Conclusion: A is Liar. B,C,D are Knights. B is fiancé. H could be Knight or Liar.
Assume Cody is Knight and ignore the previous assumption that Brad is Knight:
The fiancé is A or B. If A is Knight there is an inconsistency since he claims there is only one Knight. Thus A is confirmed as a Liar (which we already knew) and there is more than one male Knight. The fiancé is B. If B is Knight then B,C,D are Knights. But if B is a Liar, D could be either. However B being a Liar is an inconsistency. So assuming Cody is a Knight leads to A Liar, BCD Knights, the fiancé is B. Heather could be either Knight or Liar.
Assume Abe and Brad are Liars: Cody now must be Liar. Dean can be Knight, but then that makes Abe's statement True. Inconsistency.
Assume Abe and Cody are Liars: fiancé must be C or D; but cannot be C since C is Liar. This leads to Dean being Knight and fiancé. Brad then is also Liar.
Conclusion: ABC Liars, D Knight and fiancé. But again, D being the sole male Knight makes Abe's statement True. Inconsistency.
So whether we start with Brad or Cody being a Knight, we reach the same conclusion.
Abe Liar
Brad Knight and fiancé
Cody Knight
Dean Knight
Heather Knight or Liar (and fiancée)
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Posted by Larry
on 2023-02-22 10:38:13 |
same
