There are precisely three brothers in the Pearson family and exactly three brothers in the Turner family.
Three of these six men are Knights, who always tell the truth; and three are liars, who always speak falsely. Neither set of 3 brothers from the two families consist exclusively of liars.
They made the following statements:
- Abner: "Both of my brothers are liars."
- Benny: "Both of my brothers are knights."
- Connor: "Abner and Benny are both liars."
- Damian: "Connor and I are brothers."
- Eldon: "Benny and I are brothers."
- Freddy: "Eldon tells the truth."
- Freddy: "Benny belongs to the Pearson family."
Determine the full names of the six men, and ascertain their types.
If Benny were a knight then all three members of his family would be knights, forcing all three members of the other family to be liars, which is forbidden. So Benny is a liar.
If Connor is a knight, then Abner is a liar (as is Benny). If Connor is a liar, then Abner. and Benny aren't both liars, but since Benny is a liar, Abner must be a knight. So Connor and Abner are of opposite types, and there are exactly two liars among A, B, and C (and exactly one among D, E, and F.)
Freddy and Eldon must be of the same type -- if Freddy's a knight then so is Eldon, and if he's a liar, then Eldon also doesn't tell the truth. That means they're both knights, because if they were both liars that would make at least 4 liars -- one too many.
Since Freddy and Eldon are knights, the third liar is Damian. Connor and Damian are not related, then, and Eldon and Benny are brothers, and Benny is Benny Pearson. Since Connor and Damian aren't brothers, and there's only one family, one of them must be Benny and Eldon's other brother AND must be a liar since Benny falsely claimed both his brothers were knights. But if Connor were the third Pearson then Abner would have to be a knight and would have to have two lying brothers, except there's only one liar left. So Connor isn't the third Pearson; Damian is.
Abner's brothers are then Freddy and Connor, and since Freddy isn't a liar, Abner IS a liar and Connor, his opposite, is a knight. Final tally:
Abner Turner - liar
Benny Pearson - liar
Connor Turner - knight
Damian Pearson - liar
Eldon Pearson - knight
Freddy Turner - knight
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Posted by Paul
on 2022-05-03 00:44:43 |
analytic solution
