Question

Three people of kaui Island are named Alice, Bob and Carol. At least one of them is a Knight and at least one is a Knave. Exactly one of them has a prize.

They made the following statements:
Alice: Bob doesn’t have the prize
Bob: I don’t have the prize
Carol: I have the prize
Using logic & truth table find that Who has the prize?

Answer 1

Answer: Alice has the prize

Explanation:

`\boxed{\begin{array}l\underline{Alice}&\underline{Bob}&\underline{Carol}&\underline{Prize}\\T&T&F&\text{Alice}\\T&F&F&\text{no possible answer}\\T&F&T&\text{no possible answer}\\F&T&T&\text{no possible answer}\\F&F&T&\text{no possible answer}\\F&T&F&\text{no possible answer}\end{array}}`

Line 1:

Alice: Bob doesn’t have the prize (T) ... either Alice or Carol

Bob: I don’t have the prize (T) ... either Alice or Carol

Carol: I have the prize (F) ... either Alice or Bob

Alice is true for all of them!

Line 2:

Alice: Bob doesn’t have the prize (T) ... either Alice or Carol

Bob: I don’t have the prize (F) ... Bob

Carol: I have the prize (F) ... either Alice or Bob

nobody satisfies all three statements.

Line 3:

Alice: Bob doesn’t have the prize (T) ... either Alice or Carol

Bob: I don’t have the prize (F) ... Bob

Carol: I have the prize (T) ... Carol

nobody satisfies all three statements.

Line 4:

Alice: Bob doesn’t have the prize (F) ... Bob

Bob: I don’t have the prize (T) ... either Alice or Carol

Carol: I have the prize (T) ... Carol

nobody satisfies all three statements.

Line 5:

Alice: Bob doesn’t have the prize (F) ... Bob

Bob: I don’t have the prize (F) ... Bob

Carol: I have the prize (T) ... Carol

nobody satisfies all three statements.

Line 6:

Alice: Bob doesn’t have the prize (F) ... Bob

Bob: I don’t have the prize (T) ... either Alice or Carol

Carol: I have the prize (F) ... either Alice or Bob

nobody satisfies all three statements.