You're heading to PerplexiCon, the world's largest free logic convention (not to be confused with the Perplexicon, the ancient book). Unfortunately, you had gotten stuck in traffic after work, and arrived late at night. As you approach a T intersection at which you could turn east or west, you stop at a gas station to ask for directions, from four individuals wearing name tags.

Look at the 4 statements below (in the column at right is the name of the person who made each statement):

 A |   If today is Thursday, then Urnst is the consistent liar.        |  Salim
 B |   If Salim just lied, then I did not sleep in today.              |  Tessa
 C |   If Tessa slept in today, then Salim is not the consistent liar. |  Urnst
 D |   If Urnst just told the truth, then there's a full moon.         |  Viola

Only 1 of the 4 people is telling the truth. Remove the name of the truth-teller and place the names of the remaining 3 in the same order in the next board, (for example, if Tessa is telling the truth, Tessa will be removed and in the next board you will place the names Salim (in line E), Urnst (in line F), and Viola (in line G) in the column at right.

 E |   If today is Friday, then I slept in today.                      |
 F |   If I was in position B above, then there's a full moon.         |
 G |   If there's a full moon, then Urnst was in position F above.     |

Only 1 of the 3 people is telling the truth. Remove the truth-teller from the line-up and proceed as above with the 2 remaining names.

 H |   If I'm not Salim, then you should not head east.                |
 I |   If I'm not Viola, then you should not head west.                |

Only 1 of the 2 people is telling the truth.

Who is the consistent liar? Which way is the convention center? Is it raining? Is there a full moon?

Part II:

What if the nots above were removed?

(In reply to Stuck on Part I (where did I go wrong?) by Steve Herman)

To paraphrase Hamlet, material conditional, or material biconditional, that is the question.

If the former, then only the person who starts with the truth then tells a lie is lying. If the latter then both the consistent truth teller, and the consistent liar, tell the truth.

But then: 'Only 1 of the 4 people is telling the truth.'

If material conditional, then 3 statements in the first part must start with the truth, then tell a lie, and the 4th must be consistently false, to result in a true statement.

If material biconditional, then the consistent liar tells the truth, and exactly one part of every other statement is truthful.

In either case, the only person who makes a truthful statement is the consistent liar, and no-one is consistently telling the truth. The result automatically follows that the consistent liar is removed as the 'truth teller' in round 1.

Unless, of course, there is no consistent liar....

 

Edited on September 22, 2014, 1:53 am

Posted by broll on 2014-09-22 01:46:39