6.1 Floor and Flat-Based Puzzles

6.1 Floor and Flat-Based Puzzles

Floor and flat-based puzzles represent one of the most prominent, high-scoring puzzle archetypes in the Reasoning Ability section of the State Bank of India (SBI) Junior Associate (Customer Support & Sales) examination. In classical linear floor arrangements, candidates map individuals onto a one-dimensional vertical stack (Ground floor 1 up to Top floor $N$). However, contemporary SBI Clerk Preliminary and Main examinations elevate this challenge into a two-dimensional Cartesian coordinate grid: multi-storey buildings containing multiple flats on each floor.

In an SBI Clerk Prelims shift, a single floor-and-flat puzzle set carries 5 objective questions (accounting for 14.3% of the 35-mark Reasoning section). In the Main Examination, puzzles sit in the Reasoning Ability & Computer Aptitude section (60 marks for 50 questions, an average of 1.20 marks per question) and frequently integrate secondary variables such as banking department allocations, CASA deposit balances, or regional language proficiencies. Mastering this format requires structured spatial visualization, rigorous clue translation, and parallel-case tracking.

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Anatomy of the Floor & Flat Coordinate System

The standard SBI Clerk setup defines a multi-storey building with $N$ storeys (typically 4 floors) and 2 flats per floor, creating $2N$ discrete residential units (e.g., 8 positions for 4 floors $\times$ 2 flats).

The Vertical Dimension: Floors

• Floors are numbered consecutively from the base upward: the bottom floor is numbered 1, the floor immediately above it is 2, continuing up to the topmost floor numbered 4.
• When a clue specifies an "even-numbered floor," the permissible indices are Floors 2 and 4.
• When a clue specifies an "odd-numbered floor," the permissible indices are Floors 1 and 3.

The Horizontal Dimension: Flats

• Flats on each floor are positioned along an east-west axis: standard problem text specifies that Flat 1 is to the west of Flat 2 (or Flat A is west of Flat B).
• Flat 1 forms the left (western) vertical column, while Flat 2 forms the right (eastern) vertical column.
• Every living space can be mapped uniquely as an ordered pair: $(\text{Floor}, \text{Flat})$.

Cardinal Vector Navigation

Exam clues frequently employ directional geography rather than numerical coordinates:

• "Directly East / West": Must be on the same floor. If $X$ lives to the east of $Y$, $X$ occupies $(k, 2)$ and $Y$ occupies $(k, 1)$ on floor $k$.
• "Directly North / South": Must be in the same flat column. If $P$ lives south of $Q$ in the same flat, $\text{Floor}(P) < \text{Floor}(Q)$ and $\text{Flat}(P) = \text{Flat}(Q)$.
• "North-East of": Requires both a higher floor and an eastern flat. If $M$ lives north-east of $N$, then $\text{Floor}(M) > \text{Floor}(N)$, with $M$ in Flat 2 and $N$ in Flat 1.
• "South-West of": Requires both a lower floor and a western flat. If $K$ lives south-west of $L$, then $\text{Floor}(K) < \text{Floor}(L)$, with $K$ in Flat 1 and $L$ in Flat 2.

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Deciphering Spatial Clues & SBI Exam Traps

The wording of floor-and-flat puzzle clues contains subtle linguistic distinctions. Misinterpreting a single modifier will distort the entire grid.

Trap 1: "Immediately above / below" without specifying flats

[!WARNING] The Missing Flat Trap: If a clue states "A lives immediately above B", candidates frequently assume $A$ and $B$ must reside in the identical flat column. This is a critical error! Unless the clue explicitly adds "in the same flat", $A$ can reside in either Flat 1 or Flat 2 on the floor immediately above $B$ ($(\text{Floor}(A) = \text{Floor}(B) + 1)$).

Trap 2: "Number of floors between" vs. "Number of persons between"

• "Two floors are between A and B": This is a purely mathematical floor-level relationship: $|\text{Floor}(A) - \text{Floor}(B)| = 3$ Between Floor 4 and Floor 1, there are exactly two intervening floors (Floors 2 and 3). Whether $A$ and $B$ live in Flat 1 or Flat 2 is completely unconstrained.
• "Two persons live between A and B in the same flat": This restricts both the floor distance ($|\text{Floor}(A) - \text{Floor}(B)| = 3$) AND forces $\text{Flat}(A) = \text{Flat}(B)$.
• "Two persons live between A and B": Without the "same flat" qualifier, this clue can be ambiguous unless total occupants are sequenced linearly; banking exam setters almost universally phrase floor gaps using "floors between" to maintain mathematical precision.

Trap 3: "Lives on an odd floor immediately above X"

If $X$ resides on Floor 2, the floor immediately above $X$ is Floor 3, which is an odd-numbered floor. If $X$ resides on Floor 1, the floor immediately above is Floor 2 (an even floor), which would violate the clue. Thus, such clues anchor $X$ to a specific floor level.

Comprehensive Clue Translation Guide

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The Dual-Possibility Matrix Tracking Technique

Under the intense pressure of the 20-minute reasoning section, relying on trial-and-error erasing leads to cognitive fatigue and time loss. Top-scoring aspirants deploy the Dual-Possibility Matrix Technique:

1. Draw Parallel Boards: Immediately construct two identical $4 \times 2$ grid tables side by side, designated as Case 1 and Case 2.
2. Identify Primary Concrete Anchors: Search for clues that limit an individual to a strict subset of coordinates (e.g., an individual on an odd floor with a fixed vertical gap to another person).
3. Branch Mutually Exclusive Placements: Place the primary anchor into Case 1 and its alternate possibility into Case 2.
4. Superimpose Rigid Multi-Cell Blocks: Locate rigid relationship blocks (e.g., $[A/E]$ in Flat 1) and test where they can physically fit in both active cases.
5. Detect Contradictions and Terminate: The moment a clue violates a physical rule in a case (e.g., trying to place someone east of Flat 2), strike out that entire case. Never erase—simply shift full focus to the surviving branch.

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Step-by-Step Worked Floor-Flat Puzzle

Problem Statement

Eight individuals—A, B, C, D, E, F, G, and H—live in a four-storey building comprising four floors (numbered 1 to 4 from bottom to top). Each floor contains two flats: Flat 1 and Flat 2. Flat 1 is immediately to the west of Flat 2. Exactly one person lives in each flat.

Clues:

1. $G$ lives on an odd-numbered floor.
2. Exactly two floors are between $G$ and $B$, and they live in different flats.
3. $C$ lives immediately below $B$ in the same flat.
4. $D$ lives to the east of $C$.
5. $A$ lives on a floor immediately above $E$, and both reside in Flat 1.
6. $H$ lives to the east of $A$.
7. $F$ lives on one of the floors above $H$.

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Step-by-Step Deduction and Case Resolution

Step 1: Analyze Clue 1 & Clue 2 (Primary Anchoring)

• $G$ lives on an odd floor (Floor 1 or Floor 3).
• Exactly two floors are between $G$ and $B$. This requires $|\text{Floor}(G) - \text{Floor}(B)| = 3$.
• In a 4-storey building, a difference of 3 is possible only between Floor 1 and Floor 4 ($4 - 1 = 3$).
• If $G$ were on Floor 3, two floors above would be Floor 6 and two floors below would be Floor 0 (both nonexistent). Therefore, $G$ must reside on Floor 1, and $B$ must reside on Floor 4.
• Since $G$ and $B$ live in different flats, this establishes two parallel cases:
  • Case 1: $G$ lives on Floor 1, Flat 1; $B$ lives on Floor 4, Flat 2.
  • Case 2: $G$ lives on Floor 1, Flat 2; $B$ lives on Floor 4, Flat 1.

Step 2: Evaluate Clue 3 & Clue 4 (Case Elimination)

• Clue 3 states: $C$ lives immediately below $B$ in the same flat:
  • In Case 1: $B$ is on Floor 4, Flat 2. Thus, $C$ must occupy Floor 3, Flat 2.
  • In Case 2: $B$ is on Floor 4, Flat 1. Thus, $C$ must occupy Floor 3, Flat 1.
• Clue 4 states: $D$ lives to the east of $C$:
  • In Case 1: $C$ is already in Flat 2 (the easternmost flat). There is no flat to the east of Flat 2! Case 1 is logically impossible and immediately eliminated.
  • In Case 2: $C$ is in Flat 1 on Floor 3. Flat 2 on Floor 3 is completely vacant. Thus, $D$ occupies Floor 3, Flat 2. Case 2 survives!

Step 3: Evaluate Clue 5 (Rigid Column Block)

• Clue 5 states: $A$ lives on a floor immediately above $E$, and both reside in Flat 1:
  • This forms an unbreakable vertical pair $[A / E]$ in Flat 1.
  • Inspecting Flat 1 in surviving Case 2:
    • Floor 4 is occupied by $B$.
    • Floor 3 is occupied by $C$.
    • Floors 2 and 1 in Flat 1 are currently vacant.
  • Therefore, $A$ occupies Floor 2, Flat 1, and $E$ occupies Floor 1, Flat 1.
  • Flat 1 is now 100% determined: Floor 4 = $B$, Floor 3 = $C$, Floor 2 = $A$, Floor 1 = $E$.

Step 4: Evaluate Clues 6 and 7 (Final Placements)

• Clue 6 states: $H$ lives to the east of $A$:
  • $A$ resides on Floor 2, Flat 1. Directly east is Floor 2, Flat 2. Thus, $H$ occupies Floor 2, Flat 2.
• Clue 7 states: $F$ lives on one of the floors above $H$:
  • $H$ is on Floor 2. The floors above Floor 2 are Floor 3 and Floor 4.
  • On Floor 3, Flat 2 is occupied by $D$.
  • On Floor 4, Flat 2 is vacant.
  • Thus, $F$ occupies Floor 4, Flat 2.
• Check $G$: In Step 1 (Case 2), $G$ was assigned to Floor 1, Flat 2, which is vacant and consistent.

Final Verified Floor-Flat Arrangement

Every clue from the problem statement is completely satisfied without conflict.