### Brain Teasers

# The Landlord

Al, Ben, Carl, and Dan live in four adjacent apartments. The apartments are set up like this:

|1|2|3|4|

with apartment 1 being the westernmost apartment and apartment 4 being the easternmost. One of the four is the landlord. Here are some facts:

1. If Carl does not live next to Ben, then Al is the landlord and he lives in apartment 1.

2. If Al lives east of Carl, then Dan is the landlord and he lives in apartment 4.

3. If Ben does not live next to Dan, then Carl is the landlord and he lives in apartment 3.

4. If Dan lives east of Al, then Ben is the landlord and he lives in apartment 2.

Who is the landlord?

|1|2|3|4|

with apartment 1 being the westernmost apartment and apartment 4 being the easternmost. One of the four is the landlord. Here are some facts:

1. If Carl does not live next to Ben, then Al is the landlord and he lives in apartment 1.

2. If Al lives east of Carl, then Dan is the landlord and he lives in apartment 4.

3. If Ben does not live next to Dan, then Carl is the landlord and he lives in apartment 3.

4. If Dan lives east of Al, then Ben is the landlord and he lives in apartment 2.

Who is the landlord?

### Hint

All four facts are in the form of "hypothesis and conclusion" statements. If the hypothesis of such a statement is false, the whole statement is true. If the conclusion is true, the whole statement is true. However, if the hypothesis is true and the conclusion is false, the statement is false. This means that each statement has either a false hypothesis or a true conclusion.### Answer

Carl is the landlord.Obviously only one conclusion is true at most. Let us suppose that all conclusions are false. This would mean that each hypothesis is also false. From facts 1 and 3, Ben lives next to both Carl and Dan, and therefore between Carl and Dan. Then either Al lives east of both Carl and Dan (contradicting fact 4) or Carl and Dan both live east of Al (contradicting fact 2.) So there must be exactly one true hypothesis, which will be paired with the one true conclusion. Obviously each of the three false conclusions is paired with a false hypothesis.

If conclusion 1 is true, then Al lives in apartment 1. But since hypothesis 4 is false, Al has to live east of Dan. So this cannot be right.

If conclusion 2 is true, then Dan lives in apartment 4. But since hypothesis 4 is false, Al must live east of Dan. So this cannot be right, either.

If conclusion 4 is true, Ben lives in apartment 2. Then, since hypotheses 1 and 3 are false, Ben lives between Carl and Dan, putting Al in apartment 4. But since hypothesis 2 is false, Carl must live east of Al. Therefore, conclusion 3 is true.

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