Facedancers

Paul Sasur and Kengo Hashimoto

(No CON rules are allowed in this problem!

Motivation

Both students were both impressed by the Dune Chronicles by Frank Herbert. Facedancers are a humanoids who have the ability to duplicate the appearnce of another humanoid by the minute control of their musclature. In one scene, the Facedancers surround a character called Duncan Idaho. The emperor, Paul Atredes, must determine the location of the true Duncan, with the help of his sister Alia and his Fremen advisor Stilgar. However, Paul is unsure at this point whether or not he should trust Stilgar or the real Duncan.

Situation

Everyone who is the same known shape is on the same side as the others of the same shape. However, Duncan is not of the same shape, for he is surrounded by enemies. Paul and his sister are the same shape (Dodecahedron), because they are from the same family, and hence they trust. Stilgar is the unknown shape to the left, because we are unsure of his allegiance. Scytale (the leader of the face dancers) is an unknown shape to the right because we are unsure of his identity. We are also using likes an dislikes for trust and distrust, respectively. "f" is the name given to the real Duncan Idaho, "a" is Paul, "b" is Alia, "c" is Stilgar, and "d" is Scytale.

Explanation of the Givens

  1. This is to say that the real Duncan Idaho is among the Facedancers.
  2. We made all the Facedancers small to further emphasize that they are not true humans, and we include Duncan within this group, because he looks the same.
  3. This says that Duncan trusts Alia.
  4. This says that two people on the same side trust the same people, unless one of the two is Duncan, since he looks to be on the other side.
  5. This says that there is at least one person within the Facedancers that Stilgar trusts.
  6. If a person hates another, then he is hated by that same person.
  7. Paul likes only one of the people among the Facedancer group.
  8. The Cube represents the Bene Gesserit order, whose members hate everybody involved (smile).