After the gold and ivory statue of Athena was damaged, it was requested that Socrates select the most qualified craftsman to undertake the necessary repairs. He interviewed four recommended craftsmen. Their statements were not all truthful. However, each of the four makes the same number of true statements and the same number of false statements. Who should Socrates select given the statements as follows:
Craftsman A
Statement 1: I do not have all the necessary tools.
Statement 2: D is the most qualified.
Statement 3: C is experienced in this type of work.
Craftsman B
Statement 1: A is the most qualified.
Statement 2: D has never worked with ivory.
Statement 3: A’s first statement is false.
Craftsman C
Statement 1: I am experienced in this type of work.
Statement 2: B is the most qualified.
Statement 3: A does not have all the necessary tools.
Craftsman D
Statement 1: C is the most qualified.
Statement 2: A does not have all the necessary tools.
Statement 3: I have never worked with ivory.
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To determine which craftsman Socrates should select, we need to analyze the statements made by each craftsman and determine their validity. Let's go through each statement and evaluate them:
Craftsman A:
Statement 1: "I do not have all the necessary tools."
If this statement is true, then Craftsman A is admitting that they lack the necessary tools for the repair. However, if the statement is false, then Craftsman A does have all the necessary tools.
Statement 2: "D is the most qualified."
If this statement is true, then Craftsman D would be the most qualified. If false, then Craftsman D is not the most qualified.
Statement 3: "C is experienced in this type of work."
If this statement is true, then Craftsman C is experienced in this type of work. If false, then Craftsman C is not experienced in this type of work.
Craftsman B:
Statement 1: "A is the most qualified."
If this statement is true, then Craftsman A would be the most qualified. If false, another craftsman would be the most qualified.
Statement 2: "D has never worked with ivory."
If this statement is true, then Craftsman D has no experience working with ivory. If false, then Craftsman D has worked with ivory.
Statement 3: "A's first statement is false."
This statement refers to Craftsman A's first statement. If Craftsman A's first statement is true, then this statement would be false. If the first statement is false, then this statement would be true.
Craftsman C:
Statement 1: "I am experienced in this type of work."
If this statement is true, then Craftsman C is experienced in this type of work. If false, then Craftsman C is not experienced in this type of work.
Statement 2: "B is the most qualified."
If this statement is true, then Craftsman B would be the most qualified. If false, then another craftsman would be the most qualified.
Statement 3: "A does not have all the necessary tools."
If this statement is true, then Craftsman A does not have all the necessary tools. If false, then Craftsman A has all the necessary tools.
Craftsman D:
Statement 1: "C is the most qualified."
If this statement is true, then Craftsman C would be the most qualified. If false, then another craftsman would be the most qualified.
Statement 2: "A does not have all the necessary tools."
If this statement is true, then Craftsman A does not have all the necessary tools. If false, then Craftsman A has all the necessary tools.
Statement 3: "I have never worked with ivory."
If this statement is true, then Craftsman D has never worked with ivory. If false, then Craftsman D has worked with ivory.
Now, let's analyze the statements together:
- Craftsman A: If Statement 1 is true, then they do not have all the necessary tools. If Statement 1 is false, then they have all the necessary tools. Statement 2 claims that Craftsman D is the most qualified. If Craftsman A is telling the truth, then Craftsman D is the most qualified. However, Craftsman A and Craftsman D cannot both be telling the truth since they contradict each other. Therefore, Craftsman A's statements cannot all be true.
- Craftsman B: If Statement 1 is true, then Craftsman A is the most qualified. If Statement 1 is false, then another craftsman is the most qualified. Statement 2 says that Craftsman D has never worked with ivory. If Craftsman B is telling the truth, then Craftsman D has never worked with ivory. However, Craftsman B's third statement contradicts their first statement. If their first statement is false, then the third statement is true, but this means their second statement is false. Therefore, Craftsman B's statements cannot all be true.
- Craftsman C: Statement 1 claims that Craftsman C is experienced in this type of work. If this is true, then Craftsman C is experienced. Statement 2 says that Craftsman B is the most qualified. If Statement 1 is true, then Craftsman C is qualified. Their third statement claims that Craftsman A doesn't have all the necessary tools. If Statement 3 is true, then Craftsman A lacks the necessary tools. Craftsman C's statements can all be true.
- Craftsman D: Statement 1 claims that Craftsman C is the most qualified. If Statement 1 is true, then Craftsman C is the most qualified. Statement 2 says that Craftsman A doesn't have all the necessary tools. If Statement 2 is true, then Craftsman A lacks the necessary tools. Statement 3 claims that Craftsman D has never worked with ivory. If Statement 3 is true, then Craftsman D has no experience with ivory. Craftsman D's statements can all be true.
Based on the analysis above, Craftsman C's statements can all be true, while Craftsman A and Craftsman B have statements that cannot all be true. Therefore, Socrates should select Craftsman C as the most qualified craftsman for the necessary repairs.