It's my mule!
Pingy, Ross, and Mohamed are three farmers in Puzzlaria. Their farms are closely located , and they often loan each other farm animals, and tools. A mule has been passed back and forth so many times, that actual ownership of the animal has become a question. Each farmer makes two statements, one true, and one false:
Pingy said:
1. "It is Mohamed's mule."
2. "It is not mine."
Ross said:
1. "It is not Mohamed's".
2. "It is Pingy's."
Mohamed said:
1. "It is my mule."
2. "Ross's 2nd statement is false."
Who is the owner of the mule?
Pingy said:
1. "It is Mohamed's mule."
2. "It is not mine."
Ross said:
1. "It is not Mohamed's".
2. "It is Pingy's."
Mohamed said:
1. "It is my mule."
2. "Ross's 2nd statement is false."
Who is the owner of the mule?
posted by Zaux at
7:02 PM
10 Comments:
Ross owns the Mule
Anonymous ...
Ross certainly owns the mule ...
care to share your logic?
Sorry, can't explain in the elloquent way everyone seems to be able to.
It hinged on the 2nd statement of M (start with the complicated 1st). If it was his false one, then R's 2nd was True, so his 1st was False which negates it. So, M's 2nd is true, so R's 2n'd is F so it's not P's and his 1st is T so it's not M's which just leaves R ... and the other statments confirm with T/F options etc
OK ... thanks anonymous
the answer lies on pingy's statement alone.. if first statement will be marked true, the second statement will be proved to be true also which does not follow the criteria of one true and one false statement per person.. therefore, the first statement of pingy is definitely false which makes mohamed not the owner of the mule.. the second statement would then be true, the criteria, which makes pingy Not the owner of the mule also.. as two of them not the owner, it leaves ross as the owner without providing any more proof..
aldous
Either Pingy's statements OR Mohamed's statements can be used to prove that it is Ross's mule.
Let:
P = it is pingy's mule
Q = it is ross's mule
R = it is mohamed's mule
Pingy's statements:
P1: R
P2: ~P
Ross's statements:
R1: ~R
R2: P
Mohamed's statements:
M1: R
M2: ~R2 = ~P
Pingy's statements as one true, one false:
(P1 ^ ~P2) = R ^ P == bzzt
(~P1 ^ P2) = ~R ^ ~P = Q = ok
This proves that Ross owns the mule.
Ross's statements as one true, one false:
(R1 ^ ~R2) = ~R ^ ~P = Q = ok
(~R1 ^ R2) = R ^ ~P = ok
Either of these could be consistent on their own. However, the first one is also consistent with Pingy's and Mohamed's statements.
Mohamed's statements as one true, one false
(M1 ^ ~M2) = R ^ P = bzzt
(~M1 ^ M2) = ~R ^ ~P = Q = ok
This also proves Ross owns the mule. And, it is consistent with the other two gentlemen's statements as well.
This post has been removed by the author.
Each person said two statements, 0 and 1. Let P for Pingy, R for Ross, and M for me :-D.
P0: M
P1: ~P
R0: ~M
R1: P
M0: M
M1: ~R1
Each person has one false statement. The set of combinations can be represented by the following truth table (ex. 010 says that P0 R1 and M0 are true):
PRM
000: M P ~M ~P M P ---> M P
001: M P ~M ~P ~M ~P ---> ~M ~P
010: M ~P M P M P ---> M P
011: M P M P ~M ~P ---> M P
100: ~M ~P ~M ~P M P ---> ~M ~P
101: ~M ~P ~M ~P ~M ~P ---> ~M ~P
110: ~M ~P M ~P M P ---> M ~P
111: ~M ~P M P ~M ~P ---> ~M ~P
Eliminating M P's, we get:
M ~P with probability 1/5
~M ~P with probability 4/5
So, the mule is Ross's :-(.
Trail and Error FTW!
Um ... How can you depend on probability to solve a logic puzzle?
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