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A number of dacoits need to hole up in their hideout. The problem is that, as with many criminal groups, there are a number of personality conflicts that disallow certain members of the dacoit group from being in the hideout at the same time as certain other members. The personality issues of the bandits $\text{A, B, C, D, E, F, G,}$ and $\text{H}$ are illuminated by the following constraints:

  1. If $\text{D}$ is in the hideout, then $\text{E}$ is in the hideout.
  2. If $\text{E}$ is not in the hideout, then $\text{A}$ is in the hideout.
  3. If $\text{B}$ is not in the hideout, then $\text{C}$ is not in the hideout.
  4. If $\text{F}$ is in the hideout, then $\text{H}$ is not in the hideout.
  5. If $\text{A}$ is not in the hideout, then $\text{B}$ is in the hideout.

Who could be the only person in the hideout?

  1. $\text{A}$
  2. $\text{B}$
  3. $\text{E}$
  4. $\text{H}$
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Correct Answer: A

Explanation:


Who could be the only person in the hideout?

(A) $A$ could be the only person in the hideout, as shown in diagram B. While $F$ and $H$ cannot be in the hideout at the same time, they can be out at the same time.

(B) If $E$ is out, then $A$ is in.

(C) If $B$ is out, then $A$ is in.

(D, E) If $E$ or $B$ is out, then $A$ must be in. This means that $A$ must accompany $H$ or $G$ so long as either $E$ or $B$ is out. Therefore, we know (A) must be the correct answer.

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The answer is wrong, multiple answer includes A, F, H.
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