Puzzle #9: Truthteller, Liar, or Fencesitter?

There are three types of people:

  • Every statement made by a truthteller is true.
  • Every statement made by a liar is false.
  • Fencesitters alternate between true and false statements.

Laura, Paul, and Sam each might be any of the above types.  They each made two consecutive statements.  From their statements, determine each person’s type.  Warning: It is not necessarily the case that there is one of each type.

Laura:
L1: “Exactly two of us never lie.”
L2: “Paul tells the truth at most as often as Sam does.”
Paul:
P1: “Exactly two of us are one type of person.”
P2: “Laura tells the truth at most as often as Sam does.”
Sam:
S1: “Laura and Paul are the same type of person.”
S2: “I have lied.”

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, August 7, 2013 at noon Pacific Time. I will post the answer shortly after.