Twelve persons from separate cities sit in two facing rows. Answer five questions using 12 hints about how they sit, face each other and live in the cities.
The 12 Person Two-row Seating Reasoning Puzzle
Puzzle description
In a national conference, six persons Abhi, Bhuvan, Kiran, Rio, Mudra and Nila are sitting in row 1 facing south but not necessarily in the same order and each of them is from a different city among Kolkata, Delhi, Chennai, Mumbai, Pune and Bhopal. Six more persons Juhi, Somu, Vikram, Sonia, Aritra and Meera are sitting in row 2 facing north but not necessarily in the same order and each of them is from a different city among Bengaluru, Cuttack, Patna, Hyderabad, Jammu and Indore. Each person in one row faces exactly one person from the other row.
Clues:
- Abhi is third from the left end and is opposite the person who is to the immediate right of the person from Hyderabad.
- The person from Hyderabad is opposite to the person who is to the immediate left of the person from Chennai.
- The person from Bengaluru and the person from Mumbai sit at the right ends in their respective rows.
- Kiran is from Mumbai and sits adjacent to Mudra.
- Rio sits opposite to Somu and to the left of Abhi but does not sit at any extreme.
- Bhuvan is not adjacent to Rio but opposite to Juhi.
- The person from Indore sits neither at an end nor opposite to Abhi, but sits to the right of Juhi.
- The person from Patna is adjacent to neither the person from Cuttack nor the person from Jammu.
- Sonia sits at an end.
- Vikram sits opposite to the person from Delhi but sits at neither end.
- Aritra is opposite to the person from Pune, and the person from Kolkata is second to the right of the person from Bhopal.
- The person from Jammu is not adjacent to Juhi.
Questions:
Question 1. Who sits opposite to the person from Bengaluru?
- Abhi
- Mudra
- Bhuban
- Kiran
- Nila
Question 2. Which of the following five does not belong to the group formed by the rest four?
- Juhi-Kolkata
- Meera-Delhi
- Sonia-Mumbai
- Mudra-Cuttack
- Rio-Indore
Question 3. Which is the city of the person sitting three positions left of the person from Chennai?
- Pune
- Kolkata
- Delhi
- Bhopal
- Mumbai
Question 4. Which among the following is a directly opposite sitting pair?
- Juhi-Abhi
- Meera-Kiran
- Aritra-Abhi
- Vikram-Nila
- Somu-Rio
Question 5. Who are sitting on two sides of the person opposite to Abhi?
- Meera-Vkram
- Aritra-Sonia
- Juhi-Somu
- Rio-Bhuvan
- Sonia-Juhi
Time for you to answer is 20 minutes.
Hints: Identify the primary objects. Contrary to the usual assumption, primary objects are the pair of two rows of six positions facing each other. The persons sitting in the positions and the cities they are from are the two pairs of six-valued properties. Use the optimum representation for noting and analyzing the assignments. Select the clues with direct assignments first.
Defining the problem is always the first step in solving problems.
Solution to the 12 person two-row seating arrangement reasoning puzzle: Preparation
Understanding the puzzle
- Identify the primary object: Here, neither the persons nor the cities are the candidates for primary object, which is the pair of positions facing each other, the south-facing row of positions and the north-facing row of positions:
- For consistency and continuity in the numbering, the positions on the south facing rows are numbered 1, 2, 3, 4, 5, and 6. The position 6 is the rightmost for the persons sitting facing south.
- Similarly, the positions of the north-facing row are numbered 7, 8, 9, 10, 11 and 12. Position 12 is likewise the rightmost for the row of persons facing north.
- Identify the properties of the south-facing primary object and the values:
- South-facing persons: Abhi, Bhuvan, Kiran, Rio, Mudra, and Nila.
- Cities of south-facing persons: Kolkata, Delhi, Chennai, Mumbai, Pune, and Bhopal.
- Identify the properties of the north-facing primary object and the values:
- North-facing persons: Juhi, Somu, Vikram, Sonia, Aritra, and Meera.
- Cities of north-facing persons: Bengaluru, Cutttack, Patna, Hyderabad, Jammu, and Indore.
It is important to identify and remember these values to analyze the clue statements and assign breakthrough values to their correct positions.
Keeping Track of the Results of Analyzing the Clues: Assignment table
It is equally important to design the right form of assignment table to keep track of the placements of the persons and cities in their correct positions.
The most convenient assignment table:
Observe, every necessary detail is included in the assignment table. Especially important are the South-North (S < > N) and the Left-Right (L < > R) directions.
Solution to the 12 person two-row seating arrangement reasoning puzzle Stage 1: Direct Assignments First and Link Search
The strategy is to assign most at the earliest by taking up the easiest ones.
Clues identified and analyzed:
- Clue 1: "Abhi is third from the left end and is opposite the person who is to the immediate right of the person from Hyderabad": Direct assignment:
- Result: Abhi is assigned to position 3 in the row facing south three positions left from the left end.
- Alert: Left-Right direction for the two rows being different, need to be extra careful while determining which is the left and which right especially for the persons facing south.
- Hint: Mentally sit with them facing south.
- Clue 5: "Rio sits opposite to Somu and to the left of Abhi but does not sit at any extreme": Link search on assigned Abhi:
- Results: Of the two positions 1 and 2 left of Abhi, 1 being eliminated by the second part of the clue, Rio gets 2 and Somu 11 opposite to him.
- Clue 3: "The person from Bengaluru and the person from Mumbai sit at right ends in their respective rows": Direct assignments:
- Results: Bengaluru gets 12 and Mumbai gets 6 (care needed for left-right directions).
- Clue 4: "Kiran is from Mumbai and sits adjacent to Mudra": Link search on assigned "Mumbai":
- Results: Kiran gets 6 and Mudra 5 adjacent to Kiran (adjacency works both ways).
- Clue 6: "Bhuvan is not adjacent to Rio but opposite to Juhi": Link search on Rio and logical reasoning on positions:
- Results: With position 1 adjacent to Rio eliminated, the position left for Bhuvan is 4 and Juhi sitting opposite to him gets 9.
- Bonus: Sixth person in south-facing row Nila gets 1 by default.
- Alert: Don't forget to encash the bonus cheques immediately.
The first stage assignment table.
More advanced techniques and logical reasoning are needed now.
Solution to the 12 person two-row seating arrangement reasoning puzzle Stage 2: Advanced techniques and Logical Reasoning
No more straightforward assignments. Power up your reasoning.
Logical reasoning and use of horizontal and vertical bonds of placement relations:
- Clue 12: "The person from Jammu is not adjacent to Juhi": Link reference to assigned Juhi with the promise of assignment by elimination:
- Result: Right end City taken up by Bengaluru with only three probable places for Jammu—position 7, 8 or 10. The clue eliminates position 8 and 10—Jammu assigned to position 7.
- Clue 7: "The person from Indore sits neither at an end nor opposite to Abhi, but sits to the right of Juhi": Logical reasoning on placement probables:
- The clue has high promise as it refers to TWO assigned values: Abhi and Juhi.
- Result: The first part of the clue eliminates position 10 ("neither at the end" clause is not used—shows overall efficient reasoning). "right of Juhi" fixes Indore to position 11.
- Clue 8: "The person from Patna is adjacent to neither the person from Cuttack nor the person from Jammu": Horizontal bond of Patna-Cuttack and non-adjacency:
- Results: Patna-Cuttack form a horizontal bond separated by one place. The two cities must occupy positions 8 and 10.
- As Patna is not adjacent to Jammu (link reference), Cuttack assigned to 8 and Patna to 10.
- Bonus: Hyderabad to position 9 by default.
The horizontal bond of Patna-Cuttack is shown.
Continued advanced assignments.
- Clue 2: "The person from Hyderabad is opposite to the person who is to the immediate left of the person from Chennai": Vertical bond and placement reasoning:
- Result: Bhuvan living in Hyderabad (in position 4) is the person on the immediate left of the person from Chennai in position 5.
- Clue 10: "Vikram sits opposite to the person from Delhi but sits at neither end": The Vertical bond of Vikram-Delhi and position elimination:
- Results: "at neither end" eliminates probable (unoccupied) position 12. It leaves Position 10 for the pair of values "Vikram-Delhi" in a vertically bound relation.
- Clue 11: "Aritra is opposite to the person from Pune and the person from Kolkata is second to the right of the person from Bhopal": The Vertical bond of Aritra-Pune, Horizontal bond of "Kolkata-Bhopal" and use of "second to the right of" type of positional constraint:
- Results of the first part: With Mumbai blocking one end position pair (7-6), Aritra-Pune vertically bound relation assigned to position pair (12-1).
- Results of the second part: Kolkata being "second to the right of Delhi", it is assigned position 4 and Bhopal position 2.
- Alert: Avoid Directional Confusion: In two-row seating reasoning puzzles, take special care in evaluating phrases like "second to the right of" (because the right of south-facing row is left of north-facing row and your natural viewing direction is towards north).
- Clue 9: "Sonia sits at an end": Fixes Sonia to position 7 and Meera to position 8 by default.
All positions are assigned the correct values. The assignment table is filled up.
Answering the questions is now straightforward.
Answers to the questions
Question 1: "Who sits opposite to the person from Bengaluru?".
- Options: 1:Abhi, 2:Mudra, 3:Bhuvan, 4:Kiran, 5:Nila.
Answer 1: Option 5: Nila.
Question 2: "Which of the following five does not belong to the group formed by the rest four?".
- Options: 1:Juhi-Kolkata, 2:Meera-Delhi, 3:Sonia-Mumbai, 4:Mudra-Cuttack, 5:Rio-Indore.
Answer 2: Option 2: Meera-Delhi.
- All other options (Juhi-Kolkata, Sonia-Mumbai, etc.) describe a person and the city of the person opposite them, while Meera-Delhi does not fit this pattern. Meera is opposite Mudra from Chennai, not Delhi.
Question 3: "Which is the city of the person sitting three positions left of the person from Chennai?".
- Options: 1:Pune, 2:Kolkata, 3:Delhi, 4:Bhopal, 5:Mumbai.
Answer 3: Option 4:Bhopal.
- Chennai is in Position 5 (Row 1, south-facing).
- Three positions left of Chennai (from the south-facing perspective) is Position 2 (Bhopal).
- Alert! Avoid directional confusion: Left of south-facing row is the right of the north-facing row and also of the viewer.
Question 4: "Which among the following is a directly opposite sitting pair?".
- Options: 1:Juhi-Abhi, 2:Meera-Kiran, 3:Aritra-Abhi, 4:Vikram-Nila, 5:Somu-Rio.
Answer 4: Option 5:Somu-Rio. This is the only exactly opposite pair of persons.
Question 5: "Who are sitting on two sides of the person opposite to Abhi?".
- Options: 1:Meera-Vkram, 2:Aritra-Sonia, 3:Juhi-Somu, 4:Rio-Bhuvan, 5:Sonia-Juhi.
Answer 5: Option 3:Juhi-Somu.
Comments
The recommended time to solve might seem to be short. But, with experience and practice, it can be solved well within 20 minutes. Inherently, this puzzle is not hard.
In the solution, I aimed at explaining each step in details to leave no doubts in the mind of a person inexperienced in solving this type and level of reasoning puzzles.
The reasoning puzzle is from a recruitment test for Probationary Officers of State Bank of India—in short, the SBI PO test. The test is of a serious kind. This type of puzzles formed an important component for selecting persons with quick minds and strong reasoning skills.
The puzzle should also be enjoyable to both puzzle enthusiasts and puzzle lovers.
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