8 Person Three Properties Floor Stay Hard Reasoning Puzzle

8 persons stay in eight floors from 1 to 8, own 8 different mobiles and have different birth-months among 1 to 9. Can you answer 5 questions from 19 clues?

8 Person Three Properties Floor Stay Reasoning Puzzle

Description

Eight people, A, B, C, D, E, F, G and H live in eight different floors of a building. The lowermost floor is numbered 1, the one above that 2 and so on till the topmost floor is numbered 8. Each one of the persons also owns a different brand of mobile among, Nokia, Pixel, Samsung, Blackberry, Micromax, Lenovo, HTC and Oppo, but not necessarily in the same order. Each person has different birth-months from 1 to 9.

Clues:

1. Birth-month of the person who owns HTC is same as the floor number of the person who owns Lenovo, while the birth-month of the person who owns Lenovo is the same as the floor number of the person who owns HTC.
2. Only one person lives between B and the one who owns Micromax.
3. The person who lives in the topmost floor has the highest birth-month.
4. The one who owns HTC lives immediately above G.
5. G owns neither Lenovo nor Nokia.
6. E does not own HTC.
7. Only three people live between G and A.
8. The one who owns Oppo lives immediately above the one who owns Pixel, but not on the topmost floor.
9. The floor number and birth-month are the same for the persons who own Micromax and Oppo.
10. Only one person lives between F and the one who owns Samsung.
11. The number of persons living above F is the same as the number of persons living between F and D.
12. Only one person lives between the one who owns Oppo and H.
13. Birth-month of the person who owns Samsung is less than three.
14. Only two people live between C and the one who owns Nokia.
15. Birth-months of the persons who live in the topmost floor and ground floor are square numbers.
16. F lives in an odd-numbered floor above the floor numbered four.
17. Only three people live between D and the one who owns Lenovo.
18. C lives in one of the odd-numbered floors above the one who owns Lenovo.
19. The persons who live in floors numbered 4, 6 and 8 have birth-months in multiples of 3.

Questions

Question 1. Which is the BM value of the person living above H?

1. 7
2. 8
3. 2
4. 6
5. None of these

Question 2. Who lives exactly between E and D?

1. B
2. C
3. F
4. G
5. A

Question 3. Which is the mobile of the person living two floors below C?

1. Lenovo
2. Oppo
3. Nokia
4. 4. Blackberry
5. 5. None of these

Question 4. Who are the owners of Pixel and HTC?

1. A and F respectively
2. D and C respectively
3. G and B respectively
4. H and C respectively
5. None of these

Question 5. What is the mobile of the owner living three floors below the owner of Micromax?

1. Blackberry
2. Oppo
3. Samsung
4. Nokia
5. None of these

Hints:

• Make direct assignments first. Include two-values to two-positions assignments as direct assignments.
• Analyze the rest of the Clues that don't show any obvious way ahead.
• There is a way out in a simple strategy for making Clue-Implication analysis way more easy. Discover it.
• Discover the single most promising Clue to start analysis with.
• If you have come this far quickly, the rest won’t still be easy, but would be manageable.

If you can't solve it, or do solve it by any means, go through the solution. You will learn invaluable inventive methods for solving hard reasoning puzzles.

---

Solution to the 8 Person Three Properties Floor Stay Reasoning Puzzle (SBI PO): Preparation

Understanding the objects and their roles

Primary object which forms the header:

• Floor 1 to 8 is the primary object used as the header against each of which the values of the properties will be noted when assigned.

"Assigned" means placing the value in its correct position.

Secondary objects as properties which represent the rows:

• Person: A, B, C, D, E, F, G, H—forms the first row.
• Mobile: Nokia, Pixel, Samsung, Blackberry, Micromax, Lenovo, HTC, Oppo—forms the second row.
• Birth month (BM): 1 to 9—forms the third row.

Showing assignments for the property values

• Conventional approach: Vertical Floors as in real life—1 to 8 from bottom to top.
• Convenient approach: Horizontal Floors 1 to 8 from left to right with directions Down towards left and Up towards right shown with the assignment table.
• Why this arrangement: In most of the reasoning puzzles, horizontal header row and property row are used. This forms a norm that makes analysis of clues and assignments more convenient.

The assignment table at the start:

---

Solution to the 8 Person Three Properties Floor Stay Reasoning Puzzle (SBI PO): Strategies for Clue Analysis and Assignments

Stage 1: Direct assignments first

Clue 15. "Birth-months of the persons who live in the topmost Floor and ground Floor are square numbers."

• Result: BM values of Floor 1 and Floor 8 will either be 4 or 9.

Clue 3. "The person who lives in the topmost Floor has the highest birth-month".

• Result: BM value of Floor 8 is 9 and Floor 1 is 4.

Clue 19. "The persons who live in Floors numbered 4, 6 and 8 have birth-months in multiples of 3."

• Result: With Floor 8 having BM value 9, Floors 4 and 6 can have BM values either 3 or 6.

Reason for classifying Clue 19 result as a direct assignment:

BM values (3 or 6) in Floors (4 or 6) is the special arrangement of a Two-position Block and is as good as direct assignment of BM values for two Floors.

It is not yet known which of the two Floors will have BM value 3 or 6, but it is certain that Floors 4 and 6 can have no value other than 3 or 6.

The stage 1 assignment table:

Understanding Nature of the Clues: Horizontal Bonds and Fixed Bonds

Promising 5 Floor-wide bonds (more are the Floors, more promising the bond):

• Clue 7: "Only three people live between G and A".
• Horizontal Bond: "G/A-Floor-Floor-Floor-A/G".
• Clue 17: "Only three people live between D and the one who owns Lenovo".
• Horizontal Bond: "D/Lenovo-Floor-Floor-Floor-Lenovo/D".

Another example of a 4-Floor-wide Horizontal Bond:

• Clue 14. "Only two people live between C and the one who owns Nokia".
• Horizontal Bond: "C/Nokia-Floor-Floor-Nokia/C".

The remaining 16 clues (excluding Clues 3, 15 and 19 with direct assignments) have other 2-Floor-wide bonds and references between each other.

---

Conventional Method of Clue-Implication Analysis for Assignment Strategy

Usual process of getting an assignment is to analyze the implication of a promising Clue and then analyze this result against other clues and corresponding implications.

Analyzing all 16 clues, understanding the implication of each and finding a breakthrough pattern in the 15 other Clues and their implications repeatedly is cumbersome, difficult and time-consuming.

Visual representation of the Conventional Clue-Implication Aanalysis:

And so on for the other Clues trying to form complex relationships as probable configurations in each step, till conflict between probable configurations decide the breakthrough assignments.

For hard reasoning puzzles, the conventional way to analyze a large number of Clues might become extremely difficult and time-consuming—somewhat like unraveling a spaghetti.

Simple Strategy of Clue-implication Analysis for Assignments

A simple and quick way to achieve the same is:

• Deduce the implication of each Clue first to form an Implication list.
• Analyze only the implication list at each step for a breakthrough.

Visual representation of the Simple Clue-Implication Analysis Strategy:

With this novel, inventive strategy, the implication list with Clue numbers will first be formed for the 16 Clues.

Implication List from the Clues

The implications are deduced from the Clues (excluding Clue 3, Clue 15 and Clue 19):

In the implications, the values appearing on the right in the Horizontal or Fixed Bonds mean those belong to the Floors higher up ("Up direction" in the assignment table).

Implication list:

• Clue 1: BM of HTC = Floor of Lenovo; BM of Lenovo=Floor of HTC.
• Clue 2: Horizontal Bond (3 Floors): B/Micromax-Floor-Micromax/B.
• Clue 4: Fixed Bond: G-HTC (HTC immediately above G).
• Clue 5: G not (Lenovo or Nokia).
• Clue 6: E not HTC.
• Clue 7: Horizontal Bond (5 Floors): G/A-Floor-Floor-Floor-A/G.
• Clue 8: Fixed Bond: Pixel-Oppo (Oppo not in 8).
• Clue 9: BM=Floor for both Micromax and Oppo.
• Clue 10: Horizontal Bond (3 Floors): F/Samsung-Floor-Samsung/F.
• Clue 11: Floors above F = Floors between F and D.
• Clue 12: Horizontal Bond (3 Floors): H/Oppo-Floor-Oppo/H.
• Clue 13: BM for the Floor of Samsung 1 or 2.
• Clue 14: Horizontal Bond (4 Floors): C/Nokia-Floor-Floor-Nokia/C.
• Clue 16: Floor of F is 5 or 7.
• Clue 17: Horizontal Bond (5 Floors): D/Lenovo-Floor-Floor-Floor-Lenovo/D.
• Clue 18: Floor of Lenovo < Floor of C and Floor for C is 3, 5 or 7.

---

Solution to the 8 Person Three Properties Floor Stay Reasoning Puzzle (SBI PO): Advanced Techniques and Assignments

Choosing the most promising Clue as the Two-valued Clue

When the number of Clues to analyze is large with no clear pathway to solution, using a two-valued Clue as the starting point of analysis leads to an assured solution for one value or confirms rejection of one value through conflict leading to the assured solution along the second valid path.

The most promising Clue identified as the only two-valued Clue 16:

• Clue 16: "F lives in an odd-numbered Floor above the Floor numbered four":
• Result: Floor for F can only be 5 or 7.

With no bias, F in 7 probable is analyzed first.

Stage 2: Analysis for Probable Assignment of F in Floor 7

The starting assignment table at this stage:

Clue 10: Horizontal Bond (3 Floors): "F/Samsung-Floor-Samsung/F".

• Result: Samsung in 5, as Floor 9 doesn't exist.

Clue 11: "Floors above F = Floors between F and D".

• Result: D in 5, as Floors above F is 1 and Floor 5 of D is the Floor with one Floor gap below Floor 7 for F (Floor 9 doesn't exist for D in upward direction).

Clue 17: Horizontal Bond (5 Floors): "D/Lenovo-Floor-Floor-Floor-Lenovo/D".

• Result: Lenovo in 1 in downward direction (Floor 9 doesn't exist for Lenovo in upward direction).

Clue 1: "BM of HTC = Floor of Lenovo; BM of Lenovo=Floor of HTC".

• Result: HTC in Floor 4—the BM value of Lenovo person. BM of Floor 4 with HTC is 1—the Floor number of Lenovo.
• Result Invalid.

Conflict: Invalid chain of assignments (backwards):

• As BM of Floor 4 cannot be other than 3 or 6, HTC cannot be in Floor 4 with BM value 1.
• Lenovo cannot be in Floor 1.
• D cannot be in Floor 5.
• F cannot be in Floor 7.

The probable F in Floor 7 is invalid.

Critical breakthrough: F must be in Floor 5.

Intermediate assignment table for invalid probable F in 7:

Stage 3: Direct Assignments with F in Floor 5

Starting assignment table with F in 5:

Direct assignments after the critical breakthrough:

Clue 11: "Floors above F = Floors between F and D".

• Result: D in 1 (no Floor for D in upward direction with a 3-Floor gap).

Clue 17: Horizontal Bond (5 Floors): "D/Lenovo-Floor-Floor-Floor-Lenovo/D".

• Result: Lenovo in 5 (no Floor for Lenovo in downward direction).

Clue 18: "Floor of Lenovo < Floor of C. Floor for C is 3, 5,or 7".

• Result: C in 7 (only odd-numbered Floor above Lenovo Floor 5).

Clue 14: Horizontal Bond (4 Floors): "C/Nokia-Floor-Floor-Nokia/C".

• Result: With no valid Floor upwards, Nokia is in Floor 4.

Stage 3 assignment table:

Stage 4: Advanced Assignments by Analyzing Groups of Clues Creating Conflicts

Clue 7: Horizontal Bond: "G/A-Floor-Floor-Floor-A/G".

• Result: Three (G, A) probables: (G or A in Floors 2 and 6) or (A in 4, G in 8).

Clue 4. Fixed Bond: "G-HTC (HTC immediately above G)".

• Results: With no Floor available for HTC, "G in 8, A in 4" is invalid.
• G and A can only be in Floors 2 or 6.
• Probables: (For G in 2, HTC in 3, A in 6) and (for G in 6, HTC in 7, A in 2).

Clue 1: "BM of HTC = Floor of Lenovo; BM of Lenovo=Floor of HTC".

• Results: This is a Cross or X relationship between two sets of values.
• First probable: HTC in Floor 7 with BM 5 and Lenovo Floor 5 with BM 7.
• Second probable: With HTC in Floor 3, Floor 5 with Lenovo must have BM value 3 by the X relationship between Lenovo and HTC.

• But, HTC cannot be in Floor 3, as Floor 5 of Lenovo cannot have BM value 3, which is reserved for Floor 4 and 6 (by Clue 19 and Clue 3).
• Second Probable is invalid.
• First (HTC X Lenovo) valid Probable: HTC in 7 with BM 5, Lenovo Floor 5 BM 7.

Assignments after the breakthrough by the Clues 7, 4 and 1 together:

• HTC in Floor 7, BM of Lenovo Floor 5 is 7.
• G in Floor 6 (Clue 4).
• A in Floor 2 (Clue 7).

Clue 10: Horizontal Bond: "F/Samsung-Floor-Samsung/F".

• Result: Probables for Samsung are Floors 3 or 7. With HTC occupying Floor 7, Samsung in 3.

Clue 8: Fixed Bond: "Pixel-Oppo (Oppo not in Floor 8)".

• Result: Only probable: Pixel in Floor 1, Oppo in Floor 2.

Clue 12: Horizontal Bond: "H/Oppo-Floor-Oppo/H".

• Result: With Oppo in Floor 2, for H no place in downward direction. H is in Floor 4.

Clue 9: "BM=Floor for Micromax and Oppo".

• Result: BM for Oppo Floor 2 is 2. Micromax can only be in Floor 6 with BM 6. It follows BM of Floor 4 is 3 (Clue 19).
• Remaining mobile Blackberry is in only Floor left 8.

Clue 13: "BM of Samsung 1 or 2".

• Result: With Floor 2 having BM 2, Floor 3 with Samsung has BM 1.

Clue 2: Horizontal Bond: "B/Micromax-Floor-Micromax/B".

• Result: With Micromax in 6, no available Floor for B in downward direction (H in 4 blocks B), B is in Floor 8.
• Remaining person E is in only remaining Floor 3.

Clues 5 and 6 remain unused for any assignment, but the two verify the completed assignments.

The completed assignment table:

---

Answers to questions

Question 1. Which is the BM value of the person living above H?

• Options: 1:7, 2:8, 3:2, 4:6, 5:None of these.

Answer 1: Option 1: 7.

Question 2. Who lives exactly between E and D?

• Options: 1:B, 2:C, 3:F, 4:G, 5:A.

Answer 2. Option 5: A.

Question 3. Which is the mobile of the person living two Floors below C?

• Options: 1:Lenovo, 2:Oppo, 3:Nokia, 4:Blackberry, 5:None of these.

Answer 3. Option 1: Lenovo.

Question 4. Who are the owners of Pixel and HTC?

• Options: 1:A and F respectively, 2:D and C respectively, 3:G and B respectively, 4:H and C respectively, 5:None of these.

Answer 4. Option 2: D and C respectively.

Question 5. What is the mobile of the owner living three Floors below the owner of Micromax?

• Options: 1:Blackberry, 2:Oppo, 3:Samsung, 4:Nokia, 5:None of these.

Answer 5. Option 3: Samsung.

---

Comments

With large number of assignments to be deduced from heavily entangled large number of Clues, unraveling the hidden truths is difficult, to express it mildly.

But, with the two critical inventive methods, solving this apparently hard reasoning puzzle became assured and straightforward.

The critical methods essential for straightforward solution:

• Change of conventional mindset to adopt the simple Clue-Implication analysis method (by deducing the Implication list in the first step and analyzing the implication list only for breakthrough assignments).
• Choosing the two-valued Clue with two probable paths of analysis as the most promising Clue to start advanced assignments.

This hard reasoning puzzle is from a State Bank of India Probationary Officers' (SBI PO) recruitment exam and should be enjoyable to puzzle enthusiasts and puzzle lovers as well.

The solution holds rich learning potential.

---

More puzzles to enjoy

From our large collection of interesting puzzles enjoy: Maze puzzles, Riddles, Inventive puzzles, Reasoning puzzles, Paradoxes, Mathematical puzzles, Logic puzzles, Number lock puzzles, Missing number puzzles, River crossing puzzles, Ball weighing puzzles, and Matchstick puzzles.

You may also look at the full collection of puzzles at one place in the Challenging brain teasers with solutions: Long list.

Enjoy puzzle solving while learning problem solving techniques.

---