Gillis Mathematical Olympiad, 2017-2018

• Question 1 - Circle of Liars - The Truth Claim

  In a circle, `n` people are seated, each of whom is either a liar or a truth-teller.

  The people are looking towards the center of the circle. A liar always lies, and a truth-teller always tells the truth.

  Each of the people knows exactly who is a liar and who is a truth-teller.

  Each of the people says that the person sitting two places to their left (that is, next to the person sitting next to them), is a truth-teller.

  It is known that in the circle there is at least one liar, and at least one truth-teller.

  a. Is it possible that `n = 2017`?

  b. Is it possible that `n = 5778`?

  (Solution format: "word, word" for example "cat, puppy")

  Show hint

  Log in here to receive the hint
  Topics:

  Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd) Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Proof and Example -> Proof by Contradiction Logic -> Truth-tellers and Liars Problems