Floor Puzzles

A floor puzzle gives you 4–6 people and a building with the same number of floors (usually numbered 1 = ground floor upward). A set of clues tells you partial information about who lives where. You must assign exactly one person to each floor.

Draw a vertical grid — floors down the left side, person names across the top — and tick or cross each cell as you work through the clues.

1. Draw a table: rows = floor numbers (1 at bottom, 5 at top); columns = people.
2. Mark absolute clues first — e.g., "Aryan lives on floor 3" → place Aryan on 3 immediately.
3. Mark relative clues as inequalities — e.g., "Meera lives above Raj" → Meera's floor > Raj's floor.
4. Use elimination: once someone is placed, cross them out of all other floors.
5. Chain clues together — if A is above B and B is on floor 2, A must be on 3, 4, or 5.
6. Repeat until all five floors are filled.

Example 1 (5 people, 5 floors): People: Arya, Ben, Cleo, Dev, Eva. Floors 1–5. Clues:

• Ben is on floor 4.
• Arya is directly above Cleo.
• Dev is on the ground floor.
• Eva is above Ben.

Step 1: Place Dev on floor 1. Place Ben on floor 4. Eva above 4 → Eva on floor 5. Step 2: Arya directly above Cleo. Remaining floors: 2 and 3. So Cleo on 2, Arya on 3. Result: Dev-1, Cleo-2, Arya-3, Ben-4, Eva-5.

Example 2 (4 people, 4 floors): People: Anil, Bina, Charu, Disha. Floors 1–4. Clues:

• Charu is not on floor 1 or 4.
• Anil is two floors above Bina.
• Disha is on an odd-numbered floor.

Anil is two above Bina: pairs are Bina=1/Anil=3 or Bina=2/Anil=4. Disha is on an odd floor: 1 or 3. Charu is on 2 or 3. Try Bina=1, Anil=3: Disha must be on odd floor; floor 1 taken → Disha on 3, but Anil is on 3. Conflict. Try Bina=2, Anil=4: Disha on 1 or 3. Charu on 2 or 3, but 2 is Bina's → Charu on 3. Disha on 1. Result: Disha-1, Bina-2, Charu-3, Anil-4.

• "Above" vs "directly above" — "directly above" means exactly one floor higher; plain "above" means any higher floor.
• Forgetting the bottom is floor 1 — some questions say "ground floor" which equals floor 1.
• Placing someone without checking all constraints — always verify the full clue list after each placement.

1. Five people: Kia, Leo, Mia, Nat, Omar. Kia is on floor 2. Mia is directly above Leo. Omar is on the top floor (5). Nat is between Kia and Mia. Where is Leo?
2. In a 4-floor building: Priya is higher than Qais; Riya is on floor 1; Qais is directly above Riya. What floor is Priya on?

(Answers: 1 → Leo on floor 3 [Nat on 3? recalculate: Kia=2, Omar=5; Nat between Kia and Mia → Mia directly above Leo, Nat=3 so Mia=4, Leo=3 — Leo on floor 3]; 2 → Priya on floor 3 or 4; Qais=2, so Priya on 3 or 4)