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?
What if the nots above were removed?
Well, first, let's start with some basic principles.
If "A implies B" is false, then A is true and B is false.
If "A implies B" is true, then A is false or B is true (or both).
With that said, which of Statements A,B,C,D is the one that is True?
Assume A is true. Then B, C and D is false. Then (from D) U told the truth. This is a contradiction, so A is false.
Then (from A), Today is Thursday and U is not a consistent liar. Also, S, who lied, made statement E, which is true (because today is Thursday). So S did not make statement H. And the predicate (the first part) of statement H is true.
Assume B is true. Then A, C and D is false. Then (from D) U told the truth. This is a contradiction, so B is false. Then (from B) T did sleep in today. Also, T, who lied, made statement F, whose predicate is true (because T did make statement B).
Assume D is true. Then C is false. Then (from C) S is a consistent Liar. But this is a contradiction, because we know that statement E, made by S, is true. Therefore, D is false and C is true. So U made statement G. Because D is false, there is not a full moon.
E was said by S, and it is true. Thus, F and G should be false. Let's check.
F was said by T, who also made statement B. It is therefore false, because it is not a full moon.
G was said by U. But it is not a full moon, so this statement is also true.
So, E and G both seem to be true. Have I gone wrong somewhere, or is this puzzle flawed?