Track / Stage 2 / 33 of 320 #353 of 2604

Problem 353

Combinatorics Difficulty 2.0 Find the answer CEMC Cayley · Canada · 2007

On an island there are two types of inhabitants: Heroes who always tell the truth and Villains who always lie. Four inhabitants are seated around a table. When each is asked “Are you a Hero or a Villain?”, all four reply “Hero”. When asked “Is the person on your right a Hero or a Villain?”, all four reply “Villain”. How many Heroes are present?

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.