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Twelve persons live in a five-floor building such that the bottommost floor is numbered 1, the floor just above it is numbered 2, and so on till the topmost floor, which is numbered 5. Each floor has four flats—J, K, L and M from west to east respectively. Flat K is to the east of flat J and to the west of flat L, which is to the west of flat M. Eight flats are vacant. Note: (1) At least two but not more than three persons live on each floor. The adjacent flats are not vacant. Adjacent flats are immediate left, immediate right, immediately above and immediately below. (2) If it is given that A lives immediately above/immediately below B's flat, then either a vacant flat is between A and B or there is no vacant flat (no floor) between A and B. U lives on an even-numbered floor below the 3rd floor. W lives to the east of U but not in flat M. Only one floor gap is between W and P, who lives to the west of S but not immediately west. U and P live in different named flats. R lives above S and adjacent to one of the vacant flats. R and W live in different named flats. O lives to the west of R and east of V. Q lives immediately below O's flat. T lives to the east of Q. Only one floor gap is between T and Y. T lives immediately above Y's flat. Z lives just northwest of X. Which of the following statements is not true?
- Z and P live in the same named flat
- Only one flat is vacant on floor 2
- P lives on an even-numbered floor
- On floor 2, an even number of persons live
Correct answer: On floor 2, an even number of persons live
Solution
This is a floor-and-flat arrangement puzzle with multiple relative-position constraints. After placing the people consistently, floor 2 does not have an even number of persons, so that statement is false. The other statements remain consistent with the arrangement.
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