Four siblings, four doors
One day, a suitor wanted to marry Brenda. Upon arriving at her house, he encounters four doors. Brenda is behind ONE of the four doors while behind each of the other three are her brothers, Benedict, Bob and Brian. He is only allowed to open one of the four doors and if Brenda is behind that door, they would tie the knot. However, if he sees any of her brothers, he would be alone.
To help him, each door has a statement written on it:
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Door 1: Brenda is behind this door.
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Door 2: Brenda is behind door 3.
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Door 3: One of Brenda's brothers is behind this door.
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Door 4: One of Brenda's brothers is behind this door.
More than half of the statements are false. Where is Brenda?
A. Door 1 B. Door 2
C. Door 3 D. Door 4
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1 solution
Observe the satements on doors 2 and 3. They directly contradict each other so they must have opposing truth values - one must be true and the other false. Suppose the statement on door 2 is true. Then Brenda is indeed behind door 3. But this would validate the statment on door 4 as well which violates the given condition that more than half of the four statements are false (i.e. at least 3 false statements and at most 1 true statement).
So the statement on door 2 must be false while that on door 3 is true. Since there can be at most one true statement among the four, the statement on doors 1 and 4 must both be false. The negation that one of Brenda's brothers is behind this door (door 4) is Brenda herself is behind door 4.
Hence, D .