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?

If the nots were omitted from the statements, then the direction to the convention center could not be ascertained, unless it was also given that phase of the moon had not changed between and during the first and second set of statements.

Given that it had not changed, it can be educed that:
Urnst is the first truth-teller,
Viola is the second truth-teller,
Tessa is the third truth-teller,
Salim is the consistent liar,
the convention center is to the west,
it may, or may not, be raining, and
there is no full moon.

Edited on September 25, 2014, 10:18 pm

Posted by Dej Mar on 2014-09-25 22:17:03