We know that Liars always lie about everything, Knights always tell the truth. and Knaves strictly alternate between lying and telling the truth.

Let us define a new category, a Coquin, who is a renegade and will answer the questions any way he sees fit, but taking good care not to be mistaken with a Knight, Knave, or Liar. (Thus, a coquin will never make just one or two statements; he will always make three or more.)

Five workers (a blacksmith, a fisherman, an orange picker and two shepherds) are engaged in conversation. Two of them are Knights, one a Liar, one a Knave, and the other a Coquin. They say:

EIDNAS:
1. The Orange Festival is the most important event of the season.
2. The fisherman is the youngest amongst the five of us.
3. I am the Blacksmith.
4. Vaileres is not the second oldest among us.

GNIDNATS:
1. I am not the orange picker.
2. At least one of Eidnas� statements is true.
3. Inopmas is not the fisherman.
4. I am not the oldest amongst all the five of us.

INOPMAS:
1. Vaileres is the oldest amongst us.
2. I am the second oldest among us.
3. Picking oranges requires great skill and I do it well.
4. Gnidnats is not a Knave.

PITUSLON:
1. The blacksmith is the third oldest amongst us.
2. Eidnas� statements are not all false.
3. I am the older of the two shepherds.

VAILERES:
1. I am the oldest amongst the five of us.
2. I am a shepherd.
3. Pituslon�s second statement is true.
4. I am not the fourth youngest amongst all of us.


Determine who are Knights, who is the Liar, who is the Knave and who is the Coquin. What is the job of each person and what is their rank in age?

Let's write E, G, I, P, and V, for each person.

If G is a liar, G2 is false, and then E is also a liar; thus, G isn't a liar. If P is a liar, P2 is false, and then E is also a liar: thus, P isn't a liar. If V is a liar, V3 is false, and then P2 is false, and then E is also a liar; thus, V isn't a liar. If E is a liar, P2 and V3 are false, so I is a Knight (and so is G), and I1 is true, and V1 is true, making E4 true; that's illogical, so E isn't the liar either. THUS, I IS THE LIAR. I1 is false, so V1 is false; P2 is true, so V3 is true. Thus, V IS THE COQUIN, and then E AND P ARE KNIGHTS.

Knowing who is who makes it easy to deduce their jobs and relative ages -- this is left as an exercise for the reader!

Posted by Federico Kereki on 2006-07-11 21:50:10