Eight persons stay in 8 floors numbered 1 to 8 from the bottom. Use seven clues on the relations between floor stays of the persons and answer 5 questions.
8 Person Floor Stay Reasoning Puzzle
Description
A building has eight floors numbered one to eight, in such a manner that the ground floor is numbered one, the floor above it, numbered two and so on such that the topmost floor is numbered eight. One of the eight persons A, B, C, D, E, F, G and H lives on each floor.
Clues:
- E lives above F.
- Only two persons live between the floors of C and G.
- H lives on the floor immediately above the floor of B.
- Only one person lives between the floors of E and F.
- C lives on the third numbered floor.
- Only one person lives between the floors of C and D.
- D lives on a floor below the floor of E.
Questions
Question 1. Who among the following lives on the topmost floor?
- C
- B
- H
- G
- E
Question 2. Four of the following five are alike in a certain way and hence they form a group. Which one of the following does not belong to that group?
- G
- C
- A
- D
- B
Question 3. Who among the following lives on the fifth numbered floor?
- A
- D
- B
- H
- G
Question 4. How many persons live between the floors of B and F?
- 1
- 2
- 4
- 5
- 3
Question 5. Who among the following lives exactly between the floors of C and D?
- E
- F
- A
- G
- H
Hints:
- Design the simple and most convenient assignment table, which is the key to efficient analysis of the clues.
- Use Clues that will provide direct assignments first.
- Resolve between probable floor occupation arrangements using the horizontal relationships between floor occupations.
Solution to the 8 Person Simple Floor Stay Reasoning Puzzle (SBI PO)
Understanding the problem
- Identify the primary object to be used as the header of the assignment table:
- As persons live in floors, the obvious choice of primary object is Floors.
- Values: 1, 2, 3, 4, 5, 6, 7, and 8.
- Identify the property of the primary object:
- Person living in a floor is the single property of the primary object of Floors.
- Values: A, B, C, D, E, F, G, and H.
Designing the most convenient assignment table
- The natural way to think of 8 floors is a vertical arrangement from 1 to 8. Instead, think in abstraction to represent the Floors Header row horizontally with 1 leftmost and 8 rightmost.
- To keep track of Up and Down directions, show the directions above the header row.
- Persons will form the single property row of Floors.
The simple assignment table at the start:
This arrangement makes it instinctively straightforward to record and analyze assignments to the eight unknown positions of the Person row.
Solution to the 8 Person Floor Stay Reasoning Puzzle: Stage 1: Assignments directly and with elementary logic analysis
Clue 5 provides the first direct assignment and Clue 2 referring to C provides the second assignment.
Let us move on one step further to use Clue 6 to denote two probable positions of D.
- Clue 5. "C lives on the third numbered floor": C is assigned to floor 3.
- Clue 2. "Only two persons live between the floors of C and G": Link reference technique—G is assigned to floor 6.
- Clue 6. "Only one person lives between the floors of C and D": Link reference technique—D still unassigned is placed temporarily in floor 1 or floor 5.
- Important to note: Only two such temporary probables should be used, as more than two probables will make further resolution unnecessarily complex and inefficient.
The stage 1 assignment table:
Solution to 8 person floor stay puzzle: Stage 2: Use the most promising horizontal bond to create two probable floor occupation arrangements
Analysis:
- Clues 1 and 4 create a three-floor horizontal bond of floor stay relationships between E and F.
- With a larger number of positions in the bond (Clue 3 also creates a horizontal bond, but it is two-floor wide), this is the most promising horizontal bond.
- These two Clues together create TWO (more than two must not be considered) probable floor stay arrangements.
Important to note: The bond with the larger number of positions has high promise in making critical breakthrough possible through conflict in positions claimed by other clues later.
The Clues and results:
- Clue 4. "Only one person lives between the floors of E and F".
- Clue 1. "E lives above F".
- Result: Together, the two clues create a three-floor horizontal bond "F-floor-E". These three values (two known, one unknown) can be placed in two ways only:
- Probable arrangement 1: F in 2, E in 4. Rest unchanged.
- Probable arrangement 2: F in 5 (takes up one probable position of D), E in 7 and D in 1.
The latest original status (shown only for reference) with two probable arrangements are shown in stage 2 assignment status:
Solution to 8 person floor stay puzzle: Stage 3: Critical breakthrough by conflict in positions between Horizontal bonds
The second horizontal bond is now used:
- Clue 3. "H lives on the floor immediately above the floor of B": A two-floor horizontal bond "B-H" is formed.
Fitting the new two-floor horizontal bond in each of the probable floor stay arrangements:
- Result: There is no way to place "B-H" in the second probable floor stay arrangement.
- Critical breakthrough: The correct arrangement is the Probable 1.
- Results: B in 7, H in 8 and confirmed positions of F in 2 and E in 4.
The remaining uncertainties in occupying positions 1 and 5 are resolved by the last Clue 7.
- Clue 7. "D lives on a floor below the floor of E".
- Results: D in 1 and remaining person A in floor 5 by default.
The ultimate floor occupations:
Answers to Questions:
Question 1. Who among the following lives on the topmost floor?
- Choices: 1:C, 2:B, 3:H, 4:G, 5:E.
- Answer 1. Option 3: H.
Question 2. Four of the following five are alike in a certain way and hence they form a group. Which one of the following does not belong to that group?
- Choices: 1:G, 2:C, 3:A, 4:D, 5:B.
- Answer 2. Option 1: G. Rest four live in odd-numbered floors.
Question 3. Who among the following lives on the fifth numbered floor?
- Choices: 1:A, 2:D, 3:B, 4:H, 5:G.
- Answer 3. Option 1: A.
Question 4. How many persons live between the floors of B and F?
- Choices: 1:1, 2:2, 3:4, 4:5, 5:3.
- Answer 4. Option 3: 4.
Question 5. Who among the following lives exactly between the floors of C and D?
- Choices: 1:E, 2:F, 3:A, 4:G, 5:H.
- Answer 5. Option 2: F.
Comments
- With only one property row for the floors and a relatively small number of 7 Clues, this floor stay puzzle is comparatively easier to solve.
- The reasoning puzzle is from a recruitment test for Probationary Officers of State Bank of India—in short, the SBI PO test. This type of puzzles formed an important component for selecting persons with quick minds and strong reasoning skills.
The solution creates an effective foundation for achieving simple and fast solutions of more complicated floor stay puzzles.
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