Apartment Floor Puzzle: Step-by-Step Solution

This solution deciphers the floor arrangement using the provided clues to identify who lives immediately above L.

Analyzing the Clues

• People & Floors: T, W, A, L, O, B occupy floors \(1\) (lowermost) to \(6\) (topmost).
• A's Floor: A is on an even floor (\(2\), \(4\), or \(6\)).
• T relative to A: T is immediately below A. Pair: \((A, T)\).
• W relative to O: W is immediately above O. Pair: \((W, O)\).
• O's Restriction: O is not on Floor \(1\).
• T and L Gap: Exactly one person between T and L.
• W and L Gap: Exactly one person between W and L.

Deductive Steps

1. Possible (A, T) Positions: Based on A being on an even floor (\(2\), \(4\), or \(6\)) and T being below A, the possible pairs for \((A, T)\) are: \((A=2, T=1)\), \((A=4, T=3)\), or \((A=6, T=5)\).
2. Possible (W, O) Positions: Based on W being above O and O not on Floor \(1\), the possible pairs for \((W, O)\) are: \((W=3, O=2)\), \((W=4, O=3)\), \((W=5, O=4)\), or \((W=6, O=5)\).
3. Testing Case 1: \((A=2, T=1)\).
   • With T on Floor \(1\), the condition 'one person between T and L' implies L is on Floor \(3\). (T=1, Person, L=3).
   • With L on Floor \(3\), the condition 'one person between W and L' implies W is on Floor \(5\). (L=3, Person, W=5). Note: W cannot be on Floor \(1\) as it's below L.
   • Since W (\(5\)) is immediately above O, O must be on Floor \(4\).
   • This configuration (T=\(1\), A=\(2\), L=\(3\), O=\(4\), W=\(5\)) satisfies all given conditions.
   • The remaining person, B, must occupy the last spot, Floor \(6\).
   • Resulting Arrangement: Floor 1: T, Floor 2: A, Floor 3: L, Floor 4: O, Floor 5: W, Floor 6: B.
4. Eliminating Other Possibilities:
   • Case \((A=4, T=3)\): L would be on Floor \(1\) or \(5\). Floor \(1\) is impossible due to required floor gap. L=\(5\) implies W=\(3\), which conflicts with T already being on Floor \(3\).
   • Case \((A=6, T=5)\): L would be on Floor \(3\). W would be on Floor \(1\) or \(5\). W=\(1\) requires O on Floor \(0\) (impossible). W=\(5\) conflicts with T already being on Floor \(5\).
   • Thus, the arrangement derived from Case 1 is the only valid solution.
5. Conclusion: L resides on Floor \(3\). The person living immediately above L (on Floor \(4\)) is O.