Floor and Box Stacking Puzzles

In floor puzzles, the GROUND/LOWEST floor is numbered 1 and the TOP floor is the highest number. 'Above' = higher floor number; 'below' = lower. 'Immediately above' = exactly +1 floor. Watch the trap: 'as many people above X as below Y' creates a fixed gap you can exploit. Speed method: draw a vertical ladder, top at the page-top, and fill from the most-constrained clue (usually one mentioning top/bottom or 'gap' counts). For 'odd/even-numbered floors' clues, pre-label which floors are odd to filter possibilities fast. Memory aid: 'Ground is 1, Sky is n' — never invert this unless the question explicitly numbers top as 1.

Stacked-box puzzles mirror floor logic vertically. The killer clue type: 'Only TWO boxes are between P and Q' fixes the gap to exactly 3 levels (P and Q plus two between). Translate every such clue into |posP - posQ| = gap+1. Combine with anchor clues like 'R is at the bottom' to chain positions. Speed trick: list all clues as inequalities/gaps, then place the box tied to an extreme (top/bottom) first — it has the fewest options. For 'more boxes above A than below B' type, set up a counting inequality and test the minimum case. Always verify total count equals the number of boxes before finalising.

Seven names, seven floors, one staircase, and somewhere in the clue list a tiny phrase like "three people between A and B" — that is the kind of moment that decides whether SBI PO Reasoning is your strong section or a graveyard. The trick is to attack the puzzle in the right order.

Definition: A floor puzzle is a seating-arrangement variant in which people (or objects) are assigned to a tower of floors numbered from 1 (bottom) to N (top). Your job is to nail down each person's exact floor using a mix of fixed-position clues and relative-gap clues.

Definition: A fixed-position clue says something exact — "C lives on the topmost floor," "X lives on floor 3." It pins a person down with no room for doubt.

Definition: A gap clue describes the relative distance between two people — "three people live between A and B." This is the kind of clue that tests speed, because it forces you to test only a small set of pairs.

Read Clues in Filter-Then-Gap Order

The single biggest reason students lose ten minutes on a floor puzzle is that they start with the gap clue first and end up testing every pair (1-5, 2-6, 3-7, and so on). The professional sequence is the opposite. Eat the fixed clues first, then narrow with parity / even-odd filters, and only then plug numbers into the gap equation. This filter-then-gap order routinely solves SBI PO floor sets in under 90 seconds.

In our model puzzle:

• "C on the topmost floor" — a fixed clue. Lock C = floor 7.
• "A on an even floor" — a parity filter. A ∈ {2, 4, 6}.
• "B above A with three people between" — a gap equation. Number of people between A and B is 3, so the gap of floor numbers is 4. Therefore B = A + 4, with B above A.

Notice how the gap equation only kicks in after the filter has already shrunk A's options.

Walk Through the Worked Example

Question: Seven people live on floors numbered 1 (bottom) to 7 (top). Clues: A lives on an even floor; three people live between A and B; B lives above A; C lives on the topmost floor. Find A and B.

Solution:

Step 1: Use the fixed clue. C is on the top, so C = 7.

Step 2: Apply the parity filter on A. A is on an even floor, so A ∈ {2, 4, 6}.

Step 3: Translate the gap into algebra. "Three people between A and B" means three floors stand between them, so the difference is 4. Combined with "B above A," the equation is B = A + 4.

Step 4: Substitute each surviving option for A and check if B lands inside the tower (between 1 and 7) without colliding with C.

• A = 2 → B = 6. Valid. B is below 7, no clash with C.
• A = 4 → B = 8. Invalid (no floor 8).
• A = 6 → B = 10. Invalid.

Step 5: Only A = 2, B = 6 survives.

Conclusion: A lives on floor 2 and B lives on floor 6. C, as known, is on floor 7. The remaining four people fill floors 1, 3, 4, 5 using whatever clues the rest of the question supplies.

The "Difference vs. Between" Trap

The single most common error in floor puzzles is reading "three people between A and B" as "B = A + 3." That is wrong. If three people sit between the two endpoints, you have A → person → person → person → B, which is a step of four floors. People between is one less than the floor gap. Burn this into memory: between = gap − 1, gap = between + 1.

A quick formula you can use in rough work:

Floor of upper − Floor of lower = (people between) + 1

So "three people between, B above A" gives B − A = 4, and "two people between, B above A" gives B − A = 3, and so on.

Why it matters:

SBI PO Prelims gives 35 reasoning questions in 20 minutes — a brutal 34 seconds per question — and floor / box / row sets are five-question bundles. If you do not crack the base arrangement quickly, you lose five marks in one block. Once you internalise the filter-then-gap order, those five marks become reliable. Examinations like IBPS PO, RBI Grade B Phase I, and even SBI Clerk Mains use the exact same skeleton.

Real-world example:

This is the same kind of reasoning the lift in an apartment tower uses when you press multiple floor buttons. The lift "knows" which floor you live on (fixed clue) and then computes who is above or below whom to optimise the order. When you are mentally figuring out which neighbour will get off first, you are essentially solving a tiny floor puzzle.

Common misconception:

Many students start by guessing one variable at a time and then "trying" every combination. That is a 5-minute death spiral. The cleaner approach is purely deductive: each clue should eliminate options, never create options. If a clue does not cross-out a row of your table, you have not used it yet.

A second misconception is treating "above" and "below" loosely. In SBI/IBPS papers, "above" means higher in floor number, not "immediately above." A is on floor 2 and B is on floor 6 — that satisfies "B above A" perfectly, even though they are not adjacent.

Box-Stacking Variant

If you replace "floors" with "boxes stacked on top of each other," the same logic applies with no changes. Some questions say "Box X is two boxes below Box Y" — translate immediately to "Y = X + 2" with Y above X. Floor and box puzzles are mathematically identical.

Floor (building) and box/stack puzzles are SBI PO's favourite "vertical arrangement", carrying one 5-mark set in most Prelims and reliably in Mains. They feel harder than seating only because "above/below" and "top/bottom" trip rushed candidates, and SBI layers a second variable (brand, colour, salary) or a variable stack size on top.

Frame

Number floors bottom-to-top: floor 1 lowest, floor n top. Boxes stack the same way — bottom box is lowest. Fix this once and never re-question it.

Phrase	Meaning
"immediately above"	exactly one floor higher (n+1)
"two floors below"	n − 2
"at the top / lowest"	floor n / floor 1
"gap of 2 floors between"	2 empty floors between → positions differ by 3

Method

Draw a vertical ladder (top at top). Place "top/bottom" and exact-gap clues first — they pin absolute floors. Convert "as many above X as below Y" into an equation on floor numbers. Run two cases when "above/below" lacks an exact count. Lock floors before filling any second variable.

Exam Tricks & Tips

• 🎯 "As many persons above A as below B" → set (n − floorA) = (floorB − 1) and solve; it usually fixes A and B uniquely.
• 🎯 Treat "gap of 2 floors between P and Q" as |P − Q| = 3, not 2 — this off-by-one is the classic SBI trap.
• 🎯 Slide "immediately above/below" pairs as rigid two-slot blocks, exactly like seating gap-blocks.
• 🎯 For box puzzles with box + item, build a two-column ladder and fill the second column only after positions are locked.
• 🎯 In a 7-floor puzzle, floor 4 is the exact middle — a clue like "3 floors between them, one at an extreme" forces the pair to the ends.
• 🎯 If the stack size is unknown, let "only two boxes above M" and similar clues reveal it.
• ❌ Common mistake: flipping top and bottom mid-solution — always keep the highest number at the top of your ladder.

Expected exam pattern

7 floors/boxes and 7 items, often + a second attribute. 5 questions: exact floor, who is above/below, count-between, odd-one-out. Mains may leave the count variable.

Quick recap

Number bottom-to-top, anchor on top/bottom and exact gaps, treat "gap of k floors" as difference k+1, lock positions before filling any second variable.

Cover the answer, recall, then check. 11 cards on floor & box puzzles for SBI PO.

Q1. How should you number floors to avoid errors?
A1. Bottom-to-top: floor 1 lowest, floor n highest. Keep it fixed throughout.

Q2. "There is a gap of 2 floors between P and Q" — what is |floor(P) − floor(Q)|?
A2. 3 (two empty floors sit between them).

Q3. "A lives immediately above B." Relation of their floor numbers?
A3. floor(A) = floor(B) + 1.

Q4. Which clues do you place first in a floor puzzle?
A4. Absolute ones — top/bottom placements and exact-gap statements.

Q5. In a 7-floor building, which is the exact middle floor?
A5. Floor 4 (three below, three above).

Q6. How do you use "as many people above X as below Y"?
A6. Set (n − floorX) = (floorY − 1) and solve; it usually fixes X and Y.

Q7. "Only two boxes are placed above M." M's position in a stack of 7?
A7. Position 5 (positions 6 and 7 are above it).

Q8. For a box puzzle with box + colour, what order do you solve?
A8. Lock box positions first, then assign colours to the fixed positions.

Q9. How do you treat an "immediately above/below" pair while running cases?
A9. As a rigid two-slot block that slides together until an absolute clue pins it.

Q10. If the stack size is unknown, how do you find it?
A10. Use bounding clues like "only two boxes above M" to force the minimum height.

Q11. The single most common floor-puzzle mistake?
A11. Flipping top and bottom mid-solution; keep the highest floor at the top of your drawing.