How to Solve Floor and Building (Lift) Puzzles
Solve floor and building puzzles with ground-up numbering, absolute-clue anchoring, and correct inequality vs. exact-offset handling.
Expected Interview Answer
Floor and building puzzles are solved by drawing a vertical numbered column of floors (ground or floor 1 at the bottom, matching the puzzle’s convention), fixing the person or floor with an absolute clue first, and translating “above/below” and "N floors above/below" clues into inequalities and exact offsets on that column.
These puzzles are structurally the same as box stacking, but the direction convention matters even more because “building” puzzles almost always number from the ground floor up, and a clue like "X lives above Y" only tells you an inequality, not an exact gap, unless a specific floor count is given. Resolve absolute clues first — someone on “the topmost floor” or “floor 3” — since they anchor the column, then apply “more than,” "fewer than," and “exactly N floors” clues as inequalities and offsets from that anchor. A frequent trap is a clue that restricts a range without pinning an exact floor, such as "X lives on a floor above Y but below Z" — these should be kept as an open interval until another clue (often the total floor count, or an elimination by exhaustion) narrows it to one value. As with other arrangement puzzles, once every floor is tentatively filled, cross-check the completed column against all clues, since range clues are the ones most often silently violated in a rushed solution.
- Ground-up numbering matches the puzzle’s natural convention and avoids inversion errors
- Separating inequality clues from exact-offset clues prevents over-constraining early
- A final cross-check catches range clues that get silently violated
AI Mentor Explanation
A cricket academy assigning seven dormitory floors to trainees, numbered ground floor up, fixes the trainee stated to be “on the topmost floor” first, since that absolute clue anchors the whole building. A clue like “the fast bowler lives above the spinner” is only an inequality, not an exact gap, while “the wicketkeeper lives exactly two floors above the captain” is a precise offset — keeping these two clue types distinct is exactly how floor and building puzzles are solved.
Step-by-Step Explanation
Step 1
Draw a numbered vertical column
Ground floor (or floor 1) at the bottom, matching the puzzle’s own convention — never invert mid-solve.
Step 2
Anchor with the absolute clue
Fix whoever is placed on an exact floor (topmost, floor 1, etc.) before working relative clues.
Step 3
Separate inequality clues from exact-offset clues
"Above/below" alone is an inequality; "N floors above/below" is a precise offset.
Step 4
Resolve ranges last, then verify fully
Keep open-interval clues ("above Y but below Z") flexible until other clues narrow them, then re-check the whole column.
What Interviewer Expects
- Uses a consistent ground-up (or puzzle-stated) numbering convention throughout
- Anchors with the absolute-floor clue before relative ones
- Correctly distinguishes a plain “above/below” inequality from an exact "N floors above/below" offset
- Fully re-verifies the completed floor assignment against every clue, including range clues
Common Mistakes
- Treating a plain “lives above” clue as an exact one-floor gap instead of an open inequality
- Inverting the numbering direction partway through the puzzle
- Prematurely fixing a floor from a range clue before enough other clues narrow it
- Skipping the final cross-check, silently violating an open-interval clue
Best Answer (HR Friendly)
“I draw the building as a numbered column from the ground floor up, matching whatever convention the puzzle uses, and fix whoever has an absolute floor first, since that anchors everything else. I am careful to treat a plain “lives above” clue as just an inequality, not an exact gap, and only apply an exact offset when the puzzle gives a specific number of floors. Range clues I leave open until other clues narrow them, and I always finish by checking the complete floor assignment against every clue, including the range ones.”
Follow-up Questions
- How would you handle a puzzle where the building has a known total number of floors but it is not explicitly stated upfront?
- How does a “lives on an even-numbered floor” clue change the solving approach?
- What is the fastest way to narrow an open-interval clue once other floors are fixed?
- How would you extend this method to a puzzle involving two separate towers?
MCQ Practice
1. A building has 7 floors, numbered 1 (ground) to 7 (top). P lives on the topmost floor. Q lives exactly three floors below P. Which floor does Q live on?
P is on floor 7 (topmost); "exactly three floors below" is an offset of 3, so Q is on floor 4.
2. In a floor puzzle, the clue "X lives above Y" (with no floor count given) should be treated as:
Without a stated floor count, "above" is only an inequality (X’s floor > Y’s floor); the exact gap remains undetermined until another clue fixes it.
3. What should be resolved first in a floor and building puzzle with mixed absolute, relative, and range clues?
An absolute clue fixes one exact floor, giving a stable reference point from which relative and range clues can then be resolved by elimination.
Flash Cards
Standard numbering convention for building puzzles? — Ground floor (or floor 1) at the bottom, numbered upward, matching the puzzle’s own wording.
What does a plain “lives above” clue tell you? — Only an inequality — the floor number is greater, with no exact gap unless stated.
How to treat “exactly N floors above”? — A precise numeric offset of N floors, unlike the vague “above” inequality.
How to handle a range clue like “above Y but below Z”? — Keep it as an open interval until other clues or elimination narrow it to one floor.