MATH SOLVE

2 months ago

Q:
# On an island where knaves never tell the truth and knights always tell the truth, you meet 3 of the island's inhabitants: Fred, George, and Quincy. You ask Fred, "Are you a knave?" Fred says the answer to the other natives, but you can't hear him. George turns to you and says that Fred denied being a knave. Quincy says Fred is a knave. How many of the three are knaves?

Accepted Solution

A:

Answer:There is one knaveStep-by-step explanation:Let's analyze the two possible scenarios, from the unheard Fred's answer - SCENARIO 1: Fred is a knave.If Fred is a Knave, he must have told to the other natives that he wasn't, remember that Knaves will never tell the truth. In that sense, George said that Fred denied being a knave, he would be telling the truth (Fred is a knight) and Quincy said that Fred is a knave, which would also be true (Quincy is a knight too).-SCENARIO 2: Fred is a knightIf Fred is a knight, he must have told to the other natives that he wasn't a knave, he would be telling the truth. In this case, George would also be telling the truth by ensuring that Fred denied being a knave (Fred is a knight). However, Quincy would be lying to ensure that Fred is a knave. In this scenario Quincy is the knaveIn conclusion, in both scenarios, there is only one knave.