This problem involves logical deduction to determine the floor number where person Y lives based on a set of clues about seven people living on seven floors.

Step-by-Step Floor Deduction

1. Initial Setup: There are 7 floors, numbered \(1\) (lowermost) to \(7\) (topmost). We need to find the floor for Y.

2. V's Position: The clue states V lives on floor \(2\).

   • Floor \(2\): V

3. U's Position: Two people live between V (floor \(2\)) and U. This implies U must be on floor \(2 + 2 + 1 = 5\).

   • Floor \(5\): U
   • Floor \(2\): V

4. X's Position: X lives immediately below U. Since U is on floor \(5\), X must be on floor \(4\).

   • Floor \(5\): U
   • Floor \(4\): X
   • Floor \(2\): V

5. S and T's Position: S lives immediately above T. This pair (S, T) needs two adjacent, unoccupied floors. The currently occupied floors are \(2\), \(4\), and \(5\). The available floors are \(1\), \(3\), \(6\), and \(7\). The only adjacent pair possible from the available floors is \(7\) and \(6\). Therefore, S lives on floor \(7\) and T lives on floor \(6\).

   • Floor \(7\): S
   • Floor \(6\): T
   • Floor \(5\): U
   • Floor \(4\): X
   • Floor \(2\): V

6. Remaining Floors and People: The remaining floors are \(1\) and \(3\). The remaining people are W and Y.

7. Y's Constraint: Y does not live on the lowermost floor (floor \(1\)).

8. Final Placement: Since Y cannot live on floor \(1\), Y must live on the other available floor, which is floor \(3\). This leaves floor \(1\) for W.

   • Floor \(7\): S
   • Floor \(6\): T
   • Floor \(5\): U
   • Floor \(4\): X
   • Floor \(3\): Y
   • Floor \(2\): V
   • Floor \(1\): W

9. Conclusion: Y lives on floor \(3\).