9. The inhabitants of the Island of Knights and Knaves are either knights, who a
ID: 3317682 • Letter: 9
Question
9. The inhabitants of the Island of Knights and Knaves are either knights, who always tell the truth, or knaves, who always lie. While visiting the Island you encounter nine inhabitants: Bozo, Zoey, Marge, Bart, Zed, Joe, Dave, Sue and Mel. Bozo claims that it's false that Dave is a knave. Zoey tells you that Marge is a knave and Sue is a knight. Marge claims that Bozo is a knave. Bart claims, "Zed could claim that I am a knight." Zed says that only a knave would say that Dave is a knave. Joe says, It's not the case that Bart is a knave." Dave claims that Mel and Joe are both knights or both knaves. Sue tells you that Zed is a knave. Mel claims, "Neither Bozo nor Zoey are knaves." Determine, as completely as you can, whether each of the nine inhabitants is a knight or a knave.Explanation / Answer
The above can be solved conducting a hypothesis test:
Foremost, lets note the information. Knights are denoted by T meaning truth while Knaves are denoted by F meaning people who lie or are false.
1. Bozo: Dave-T
2. Zoey: Marge-F & Sue - T
3. Marge: Bozo-F
4. Bart: Zed-T
5. Zed: if Dave-F then Dave-F, thus, Dave-F
6. Joe: Bart-T
7. Dave: Mel,Joe-T or Mel, Joe-F
8. Sue: Zed-F
9. Mel: Bozo&Zoy - T
Solution:
H0: Let Joe be a knave, Joe-F
then his claim about Bart is false & thus Bart-F.
Bart claims that Zed-T is also falsefied & hence Zed-F
Then Zed's claim is also false, i.e., Dave-F
If Dave-F, then Joe & Mel can be oppsoite. Moreover, it is hypothesized that Joe-F, thus Mel-T
If Mel-T, Baze & Zoey-T
If Bozo-T, then Dave-F. Also if Zoey-T, then Marge-F & Sue-T
There are no contrasting poistions in the above hypothesis, thus the above hypothesis is True. Finally,
Knights are: Mel, Bozo, Zoey & Sue.
Knaves are: Joe, Bart, Zed, Marge & Dave.
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