Reply
Thu 11 Jan, 2007 05:48 am
A seal and four clones each makes a different statement. Two of the statements are false. Which of these is the original?
Seal A = "If I am a clone, then either C or E is telling the truth."
Seal B = "A's statement can only be false if D is the original."
Seal C = "If B or E is the original, then D is not telling the truth."
Seal D = "If I am the original, then neither A nor C is lying."
Seal E = "If A or C is telling the truth, then I'm not a clone."
False versions of their statements
Seal A = A is a clone. C and E are lying.
Seal B = D is a clone. A is lying.
Seal C = B or E is the original. D is telling the truth.
Seal D = D is the original. A or C is lying.
Seal E = A or C is telling the truth. E is a clone.
Possible False Pairs
AB: A is a clone. C and E are lying. D is a clone. A is lying. (no - 4 liars)
AC: A is a clone. C and E are lying. B or E is the original. D is telling the truth. (no - 3 liars)
AD: A is a clone. C and E are lying. D is the original. A or C is lying. (no - 4 liars)
AE: A is a clone. C and E are lying. A or C is telling the truth. E is a clone. (no - 3 liars)
BC: D is a clone. A is lying. B or E is the original. D is telling the truth. (no - 3 liars)
BD: D is a clone. A is lying. D is the original. A or C is lying. (no - 3 liars)
BE: D is a clone. A is lying. A or C is telling the truth. E is a clone. (no - 3 liars)
CD: B or E is the original. D is telling the truth. D is the original. A or C is lying. (no - D can't lie and tell the truth)
CE: B or E is the original. D is telling the truth. A or C is telling the truth. E is a clone. (yes)
DE: D is the original. A or C is lying. A or C is telling the truth. E is a clone. (no - 3 liars)
Therefore, C and E are lying. B or E is the original, but E is a clone. Therefore, B is the original.
Oops. I must have screwed something up. I was only verifying consistency of the false statements. However, after looking at what would be the true statements (A, B, D), A's statement is inconsistent with the proposed solution.
I don't think there is a solution. If X then Y is false only when X is true and Y is false.