8 Students 8 Subjects Circular Seating Reasoning Puzzle

8 students studying 8 different subjects are sitting in an 8 position round table, all facing away from center. Solve the reasoning puzzle from 14 Clues.

8 Students 8 Subjects Circular Seating Reasoning Puzzle

Description

Vicky, Piklu, Abhi, Nina, Sam, Sonia, Sree and Ritu are eight friends studying in colleges in different streams like Maths, Physics, Economics, Chemistry, Psychology, Physiology, Botany and Zoology, but not in the same order. All of them are seated around a circular table, facing away from the center.

Clues:

1. Vicky sits third to the left of the person who studies Psychology.
2. Only two persons sit between Sam and Sree.
3. Neither Sam nor Sree studies Psychology and neither of them is an immediate neighbor of Vicky.
4. The person who studies Zoology sits second to the right of Nina.
5. Nina is not an immediate neighbor of Vicky.
6. Nina does not study Psychology and Vicky does not study Zoology.
7. The one who studies Maths sits third to the left of Sonia.
8. The one who studies Maths and the one who studies Psychology are not immediate neighbors.
9. Only one person sits between Nina and the one who studies Economics.
10. The person who studies Chemistry and the one who studies Physics are immediate neighbors.
11. Only one person sits between Piklu and the one who studies Physiology.
12. The one who studies Physiology is an immediate neighbor of Ritu.
13. Sree and Piklu are not immediate neighbors.
14. Nina does not study Physics.

Questions

Question 1.

How many people sit between Sam and the one who studies Physiology (when counted in clockwise direction from Sam)?

1. one
2. two
3. three
4. four
5. five

Question 2.

Who studies Economics?

1. Abhi
2. Sonia
3. Piklu
4. Vicky
5. Sam

Question 3.

Which of the following combinations is definitely true?

1. Nina -- Psychology
2. Abhi - Physiology
3. Sree - Economics
4. Piklu -- Chemistry
5. None of the above

Question 4.

Who studies Maths?

1. Vicky
2. Sam
3. Piklu
4. Abhi
5. Nina

Question 5.

What is the position of the person who studies Botany with respect to Abhi?

1. Immediate left
2. Second to the left
3. Third to the right
4. Third to the left
5. Second to the right.

Hints:

• Design the most convenient assignment table to record who sits where and studies which subject.
• Place maximum number of students related positionally first. In a circular seating puzzle, the first placements can be in any position. All later positioning will be relative to the first placements.
• Be alert for the left and right directions of sitting.
• Use Clues creating two-position blocks and horizontally related students for breakthroughs.
• Identify and use the Clue that would provide the critical breakthrough at the right time. Unless, the critical breakthrough Clue is applied at the right time, solution will get difficult.

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Solution to the 8 Students 8 Subjects Circular Seating Reasoning Puzzle

The circular table with 8 students in 8 positions, all facing away:

Assignment table:

Linear side-by-side equivalent seating arrangement, as assignments in a circular arrangement is impracticable.

In abstract form, the circular table of 8 positions is represented by a linear table with positions 1 to 8 and end positions 1 and 8 adjacent (folded linear table).

• Columns: Positions 1 to 8.
• Rows: Students and Subjects. Row values to be assigned to the column positions.
• Facing and Right/Left directions: With all students facing out, natural left of the linear assignment table will be the natural clockwise direction, but on the RIGHT for the persons seating. Similar with natural right/anti-clockwise/LEFT for a Student.

The assignment table to be used:

Stage 1: First Assignments by Horizontal Bond, Neighboring Clues and Two-position Block

Clue 1. "Vicky sits third to the left of the person who studies Psychology."

• Vicky is placed arbitrarily in position 5, Psychology in 2 to anchor the grid. Other placements will be relative to these first placements.

Assignments by this Clue selection splits up the total number of positions into three similar sized parts. This is desirable, as it increases the future possibilities of assignments by constraints on occupying of positions.

Clue 2. "Only two persons sit between Sam and Sree."

• Horizontal Bond: Sam/Sree - position - position - Sree/Sam (both ways bond).

Clue 3. "Neither Sam nor Sree studies Psychology and neither of them is an immediate neighbor of Vicky" → breakthrough by neighboring Clue.

• With positions 2, 4 and 6 inaccessible to either Sam/Sree, the only two feasible positions for the two-position block of Sree/Sam are 3 and 8 (clockwise).

A two-position block is valuable, as it not only ensures no other value can occupy the two blocked positions, it also ensures blocked values cannot occupy other positions.

Clue 5. "Nina is not an immediate neighbor of Vicky" → link reference to already assigned Vicky and a neighboring Clue.

• Nina in 1, 2 or 7.

Clue 6. "Nina does not study Psychology and Vicky does not study Zoology" → further reference to Nina decreases number of probable positions Nina can occupy.

• Nina in 1 or 7. Vicky in 5 "not Zoology".

Clue 4. "The person who studies Zoology sits second to the right of Nina" → Vicky second to the right of Nina in 7 does not study Zoology → Nina cannot be in 7.

• Nina in 1, Zoology in 7.

Clue 9. "Only one person sits between Nina and the one who studies Economics."

• Economics in 3, the only valid position available.

Stage 1 assignments:

Stage 2: Link reference, Neighboring Clue and Horizontal Bonds

Clue 7. "The one who studies Maths sits third to the left of Sonia."

• Sonia in 2 or 6, Maths in 5 or 1.

Clue 8. "The one who studies Maths and the one who studies Psychology are not immediate neighbors."

• Sonia in 6 is invalid by Maths to be in 1, neighboring Psychology → Sonia in 2, Maths in 5.

Stage 2 assignments:

Stage 3: Assignment Completion by Two-position Block, Horizontal Bond Constraints and Neighbor Restrictions

Clue 10. "The person who studies Chemistry and the one who studies Physics are immediate neighbors."

• The Physics/Chemistry Bond can occupy positions 1 and 8 only → Forms a two-position block on Subjects in 1 and 8.

Clue 10 provides the critical breakthrough by imposing severe constraints on subjects occupying remaining positions.

Clue 11. "Only one person sits between Piklu and the one who studies Physiology."

• Horizontal Bond: Piklu/Physiology-position-Physiology/Piklu → Piklu can be in 4/6, Physiology in 6/4.

Finding the right place for Piklu has been the main bottleneck in reaching an efficient solution, now simplified by the two-position block on Chemistry/Physics on 1 and 8.

Clue 12. "The one who studies Physiology is an immediate neighbor of Ritu."

• With Physiology in 4, Ritu couldn't have been its neighbor → Physiology must be in 6 and Piklu in 4.
• Ritu in 7, Abhi in 6 by default as the only person and position left to be assigned.

Clue 13. "Sree and Piklu are not immediate neighbors" → Identifies position 3 not for Sree (as Piklu is in 4).

• Sree in 8, Sam in 3.

Clue 14. "Nina does not study Physics" → Resolves Chemistry for Nina in 1.

• Sree/Physics in 8.
• Botany goes to Piklu in 4 by default.

Completed assignments:

Completed assignments in vertical table form:

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Key deductions

Stage 1: First Assignments by Horizontal Bond, Neighboring Clues and Two-position Block

• Clue 1: "Vicky sits third to the left of the person who studies Psychology" → Anchored the grid: Vicky in 5 Psychology in 2.
• Clues 2 + 3: Two-position block Sree/Sam in 3 and 8.
• Clues 5 + 6 + 4: Position elimination: Nina in 1, Zoology in 7.
• Clue 9: "Only one person sits between Nina and the one who studies Economics" → Link reference to Nina → Economics in 3.

Stage 2: Link reference, Neighboring Clue and Horizontal Bonds

• Clues 7 + 8: Position elimination by constraints: Sonia in 2, Maths in 5.

Stage 3: Assignment Completion by Two-position Block, Horizontal Bond Constraints and Neighbor Restrictions

Clue 10 provides critical breakthrough by severely reducing probable positions for other subjects.

• Clue 10: Two-position Block Physics/Chemistry in 1 and 8 → provides the critical breakthrough.
• Clues 11 + 12: Horizontal Bond and Neighboring constraints → Piklu in 4, Physiology in 6, Ritu in 7, Abhi in 6 by default.
• Clue 13: "Sree and Piklu are not immediate neighbors" → Neighboring constraints → Sam in 3, Sree in 8.
• Clue 14: "Nina does not study Physics" → Two-position block of Chemistry/Physics in 1 and 8 formed by Clue 10 resolved → Chemistry in 1, Physics in 8. Botany in 4 by default.

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Answers to the questions

Question 1. How many people sit between Sam and the one who studies Physiology (when counted in clockwise direction from Sam)?

• Answer 1. Option 4: four (Clockwise means natural left in this case with positions 1 and 8 adjacent for the circular table).

Question 2. Who studies Economics?

• Answer 2. Option 5: Sam.

Question 3. Which of the following combinations is definitely true?

• Answer 3. Option 2: Abhi - Physiology → Nina – Psychology, Sree - Economics, Piklu – Chemistry are invalid relations between Student and Subject studied.

Question 4. Who studies Maths?

• Answer 4. Option 1: Vicky.

Question 5. What is the position of the person who studies Botany with respect to Abhi?

• Answer 5. Option 5: Second to the right (Clockwise or natural left is on the right for person sitting Abhi).

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Comments

• All Students sitting Facing away from the center provided the advantage of reduced difficulty in deducing right and left directions.
• First assignments by horizontal bond between two values and same stage assignments by two-position block resolution by neighboring clue constraints.
• Overall, neighboring constraints provided majority of the breakthroughs.
• The turning point in the efficient solution has been the critical breakthrough by Clue 10 at the right time.

The circular seating reasoning puzzle is from an SBI PO recruitment exam for selecting quick and young minds.

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