Angelo Archbald finds himself on a remote island, which is entirely populated with precisely two types of people. These are the Knights, who always tell the truth and Liars, who always speak falsely.
Angelo notices some natives nearby and decides to speak to them in order to deduce their types.
The conversation is as follows:
- Angelo Archbald: "Are you mute?"
- Louis: *shakes head*
- Laverne: *shakes head*
- Lauren: "Exactly one of Louis and Laverne is mute".
- Leon: "Louis and I are both Liars or both are Knights. Same with Linda and I".
- Linda: "The only Liar is either Laverne or Leon."
Who are the Knights? Who are the Liars? Who is/are mute?
Provide adequate reasoning for your answers.
Assuming that *shakes head* means "no".
Lauren's statements indicate that Louis and Linda must be knights because Leon is claiming they are of the same type as he is. If Leon is a knight the other 2 are knights. If Leon is a liar, then the other two are not liars as the liar is claiming.
Since Linda is a knight, there is only one liar and it isn't Lauren, so Lauren must be a knight.
If Lauren is a knight, then exactly one of Louis and Laverne is mute and yet they both claim to be not mute, so one of them is lying, and per Linda that liar is Laverne.
None of Lauren, Leon, and Linda are mute, since they all spoke.
So far we know:
Laverne is a Mute and a Liar.
Everyone else is a Knight and can speak.
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Posted by Larry
on 2023-02-11 11:53:48 |
Solution
