9 Person 9 Preference Circular Seating Reasoning Puzzle

Nine persons who prefer 9 different travel destinations sit on a circular table, four facing away and the others facing towards center. Solve from 17 Clues.

9 Person 9 Preference Circular Seating Reasoning Puzzle

Description

Nine people, namely Bree, Cini, Epu, Fiji, Gyan, Hal, Lipi, Monu and Rani sit around a circular table. Four of them face away from the center, and the rest face towards the center. Each of them likes to travel to a different type of place among, Hill, Forest, Temple, Beach, City, Heritage, Desert, Lake and River but not necessarily in the same order.

Clues:

1. Rani is second to the left of Lipi who doesn't like to travel to places of types Heritage, Desert, Hill.
2. Monu likes to travel to Lake.
3. The one who likes to travel to Temple is fourth to the right of the one who likes Forest.
4. The person who likes Forest is facing away from the center.
5. Lipi is fourth to the right of Hal, whose facing direction is same as that of Cini.
6. Cini, who likes City, is sitting fifth to the left of Fiji, who is an immediate neighbor of Rani.
7. Gyan does not like Hill, Heritage or Desert type of place.
8. Epu likes Heritage travel.
9. The one who likes Desert is facing towards the center as Gyan faces but they are not neighbors of each other.
10. Desert travel is not liked by Rani.
11. Hal is facing away from the center.
12. Hill travel is not liked by Hal.
13. The one who likes Beach is sitting second to the right of the one who likes Hill.
14. Cini is second to the left of Bree who likes Forest.
15. Rani is in the group of Gyan in terms of facing direction.
16. Monu is facing away from the center and is second to the right of Epu.
17. Temple travel is liked by a person who is facing away from the center.

Questions

Question 1. Who is sitting second to the right of Bree?

1. Monu
2. Cini
3. Rani
4. Gyan
5. Fiji

Question 2. The person on the second right of Lipi likes to travel to,

1. Desert
2. Hill
3. River
4. Beach
5. Lake

Question 3. Which of the following combinations is correct?

1. Fiji-Hill-Facing away
2. Bree-Forest-Facing in
3. Rani-Lake-Facing away
4. Epu-Heritage-Facing in
5. Hal-Desert-Facing away

Question 4. Who among the following is an immediate neighbor of the one who likes Heritage?

1. The one who likes Temple
2. The one who likes Forest
3. Hal
4. Both 1 and 3
5. Fiji

Question 5. Who among the following sits third to left of the person who likes Lake?

1. The one who likes Hill
2. Cini
3. Bree
4. Epu
5. The one who likes Desert

Time to solve is 30 minutes.

Hints:

• Design optimal assignment table.
• Anchor the assignment table grid by a first Person assignment having facing direction in the Clue.
• Simplify analysis by first finding facing directions first.
• For speed, form implication list with Clue #. Henceforth analyze only the short implication list.
• Look for the critical breakthrough using conflicts caused by horizontal positional bonding relationships between Persons.
• Resolve the places liked by horizontal position relationship bonding analysis.

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Quick Solve: 9 Person 9 Preference Circular seating Reasoning Puzzle (SBI PO)

Nine persons sitting in nine numbered positions in the circular table:

The most convenient form of showing the details is a linear table with Position 1 to 9 as headers, and Person, Place and Facing as rows.

The positions 1 and 9 will be considered as adjacent to each other.

It is as if the circular table is split at the junction of positions 1 and 9 and straightened out in a linear form. The linear table, when folded with 1 and 9 joining, the circular table will be formed.

The nine position linear representation of the circular table:

This will form the header with 9 numbered positions to which the values of a Person, Place preferred and Facing direction will be assigned, The values are:

• Person: Bree, Cini, Epu, Fiji, Gyan, Hal, Lipi, Monu, Rani.
• Place (liked): Hill, Forest, Temple, Beach, City, Heritage, Desert, Lake, River.
• Facing (direction): I for facing the center, O for facing away from the center.

The corresponding convenient assignment table to be used:

Strategies to be followed:

1. Direct assignments aided by Horizontal Bond first (as End Position reference is crucial).
2. Facing direction being the key constraint, Facing directions will be identified before taking up Clue analysis.
3. To simplify Clue analysis, bare implication list with Clue # will be formed.
4. Horizontal Bond conflicts to be used for most breakthroughs.

Clue Analysis Stage 1: Anchor Positions by Horizontal Bond and End Position Reference

• Clues 14 + 4: Bree (Forest/O) in 4 → Cini in 6.
• Clues 3 + 17: Temple/O in 9.

Assignments:

Stage 2: Resolving Facing Directions

• Clues 11 + 16: Hal/O, Monu/O.
• Clues 4 + 14: Bree/O.
• Clue 5: Cini/O → All O resolved.
• Rest five Facing Direction I → All Facing directions resolved.

Clue 6.

• Cini/City/O in 6.
• Fiji/I in 2.

Assignments:

Stage 3: Implication list with Clue #

Clue 1: With both Rani and Lipi facing in, Horizontal Bond: Rani-position-Lipi; Lipi not (Heritage, Desert, hill).

Clue 2: Monu/Lake/O.

Clue 5: With Lipi/I and Hal/O, Horizontal Bond: Lipi-position-position-position-Hal.

Clue 6: Rani either in 1 or 3 (rest of the implications assigned).

Clue 7: Gyan not (Hill, Heritage, Desert).

Clue 8: Epu/Heritage.

Clue 9: Desert-Gyan not neighbors.

Clue 10: Rani not Desert.

Clue 11: Hal/O.

Clue 12: Hal not Hill.

Clue 13: Horizontal Bond (two-directional): Beach/Hill-position-Hill/Beach.

Clue 16: With Monu/O and Epu/I, Horizontal Bond: Epu/Heritage-position-Monu/Lake: Two Vertical Bonds are separated by one position in a Horizontal Bond---promising.

Join the two Horizontal Bonds in Clue 1 first and Clue 5 second:

• Clue 1 + Clue 5 + Clue 6 Implications:
• Joined Horizontal Bond: Rani-position-Lipi-position-position-position-Hal (as Lipi is common in Clue 1 at rightmost position and in Clue 5 in leftmost positions of respective Horizontal Bonds).
• Rani either in 1 or 3.
• Lipi not (Heritage, Desert, hill).

Stage 4: Breakthroughs by Horizontal Bond Conflict

• Clue 6:
  • Cini (6) is 5th left of Fiji → Fiji in 2.
  • Fiji is neighbor of Rani → Rani in 1 or 3.
• Clues 2 + 16:
  • Epu/I is 2nd left of Monu/O → Horizontal Bond: Monu/Lake --- Position --- Epu/Heritage.
• Clues 1 + 5 + 6:
  • Rani --- Position --- Lipi --- Position --- Position --- Position --- Hal Horizontal Bond chain → Rani in 1 invalid as Monu/Lake --- Position --- Epu/Heritage Horizontal Bond would have no place to fit in.
  • Rani/I in 3, Lipi/I in 5, Hal/Temple/O in 9.
  • Monu/Lake/O in 1, Epu/Heritage/I in 8.
  • Default: Gyan/I in 7.

Assignments:

Stage 5: Assign Places Liked

• Clue 10 + 1 + 7:
  • Rani ≠ Desert, Lipi ≠ Desert, Gyan ≠ Desert → Fiji/Desert in 2.
  • Fiji/Desert at 2 is forced as Rani (3), Lipi (5), and Gyan (7) exclude Desert (Clues 1, 7, 10).
• Clue 13: Beach is 2nd right of Hill → Rani/Hill in 3, Lipi/Beach in 5.
• Clue 7: Gyan ≠ Hill/Heritage/Desert → Gyan/River in 7.

Completed assignments:

Answer key:

• Answer 1. Option 5: Fiji.
• Answer 2. Option 3: River.
• Answer 3. Option 4: Epu-Heritage-Facing in.
• Answer 4. Option 4: Both 1 and 3.
• Answer 5. Option 3. Bree.

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Fully Explained Solution to the 9 Person 9 Preference Circular seating Reasoning Puzzle (SBI PO): Preparation

The Circular Table, the Objects and Showing Assignments

Nine persons sitting in nine numbered positions in the circular table:

It is not practicable to show a Person with a specific travel Place preference and his Facing in or out against a position in a circular form of assignment table.

Instead, the most convenient form of showing the details is a linear table with Position 1 to 9 as headers, and Person, Place and Facing as rows.

In the abstract representation of the circular table to a linear table will have one specific condition:

The positions 1 and 9 will be considered as adjacent to each other.

It is as if the circular table is split at the junction of positions 1 and 9 and straightened out in a linear form. The linear table, when folded with 1 and 9 joining, the circular table will be formed.

The nine position linear representation of the circular table:

This will form the header with 9 numbered positions to which the values of a Person, Place preferred and Facing direction will be assigned, The values are:

• Person: Bree, Cini, Epu, Fiji, Gyan, Hal, Lipi, Monu, Rani.
• Place (liked): Hill, Forest, Temple, Beach, City, Heritage, Desert, Lake, River.
• Facing (direction): I for facing the center, O for facing away from the center.

The corresponding convenient assignment table to be used:

Nature of the Puzzle---The Key Constraint:

• Pivot position: As a circular table has no beginning or end, the first person with facing direction discovered will be placed in any suitable position. All other placements will be relative to this Pivot position.
• [Key constraint is the Facing direction]: Unless facing direction is identified first, the Clues referring to the positional separation could not be used. [The earlier the Facing directions of the Persons identified, the easier further positional analysis will be.]

Nature of the Puzzle: The Strategies

• First Stage: Assign maximum number of positionally related Persons with Facing directions identified.
• Second Stage: In the second stage, find the Facing directions of all the Persons ignoring their positional relations. Note the Facing directions with the list of Person names at the top of the assignment table. This will make solving the puzzle simpler.
• The [Clue for identifying the Facing directions]: Use the [limit of four persons in Facing away direction] as the [key information] to find the Facing directions of all.

Nature of Clues: Horizontal and Vertical Bonds, Link References

• Use group of Clues linked by values shared:
• Examples: Clues 11 and 5 are linked by sharing "Hal", and Clues 5 and 6 are linked by sharing of "Cini". The three Clues 11-5-6 form a linked chain of Clues with promise of multiple assignments.
• Horizontal Bonds: The Clues with positional separation of property values form the Horizontal Bonds. These provide breakthroughs by availability of free positions and conflicts.
• Examples: Clues 1, 3, 5, 6, 13, 14, 16 identify Horizontal Bonds to be used in due time.
• Vertical Bonds: Clues specifying a Place liked by a Person form a Vertical Bond.
• Example: Clue 8. "Epu likes Heritage travel" forms a Vertical Bond of Person Epu with Place liked Heritage travel.

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Practices that make assignment analysis easier:

• When a Person or Place liked is assigned to its correct Position, strike out the assigned value from the list of values shown with the assignment table at every stage.
• Likewise, when all implications of a Clue are used up for assignments, strike out the Clue from the list of Clues (reducing number of Clues makes further analysis easier).

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Solution to the 9 person 9 Preference Circular seating Reasoning Puzzle (SBI PO): Clue Analysis and Assignments

Stage 1: First Direct Assignment of a Person to the Pivot Position (any position this one time only)

Clue 4. "The person who likes Forest is facing away from the center":

• Implication: Forest-loving Person is in direction O.

Clue 14. "Cini is second to the left of Bree who likes Forest":

• Assignments: Resolves Forest-loving Person as Bree facing away. Bree/Forest/O is placed in position 4 (in the middle area to reduce 1 to 9 joining analysis load).
• Cini second the left of facing away Bree is in position 6.

Clue 3. "The one who likes to travel to Temple is fourth to the right of the one who likes Forest":

• Assignment: Place liked Temple is in position 9 (after moving right towards viewer's left four positions) as position 1 and 9 are adjacent in the circular seating.

Clue 17. "Temple travel is liked by a person who is facing away from the center":

• Assignment: Person loving Temple travel in position 9 is assigned facing direction O.

Stage 1 assignments:

Stage 2: Discovering the Facing direction of All Persons

Key Information: Only four Persons face away from center.

Strategy: Identify the Clues that refer to Facing away and Facing inwards.

Clue 11. "Hal is facing away from the center":

• Implication: Hal-O.

Clue 16. "Monu is facing away from the center and is second to the right of Epu":

• Implication: Monu-O. Monu second to the right of Epu (to be used later).

Clues 14 + 4. Already assigned: Bree/Forest-O.

Clue 5. "Lipi is fourth to the right of Hal, whose facing direction is same as that of Cini":

• Implication: Cini-O. First part already taken care of.

Breakthrough: The Clues together identify the four Persons Facing away from the center: Bree-O, Cini(O), Hal(O), and Monu(O).

• Implication: The rest five Persons Epu, Fiji, Gyan, Lipi all are facing inwards: Epu-I, Fiji-I, Gyan-I, Lipi-I and Rani-I.

The Facing directions incorporated in the Person list along with the assignment table at every stage.

Immediate assignments using facing directions and linked Horizontal Bond

Clue 6. "Cini, who likes City, is sitting fifth to the left of Fiji, who is an immediate neighbor of Rani":

• Assignments:
• Cini/City/O in position 6.
• Fiji/I in position 2 (as Cini facing away in position 6 is fifth to the left of Fiji facing in).

Facing direction table:

Facing directions will be included in the Person list of all assignment tables.

Stage 2 assignment table with all facing directions identified,

Stage 3: Forming the Implication list and Joining of Horizontal Bonds

Implications of rest of the Clues are intricately woven. To simplify the complex Clue-Implication analysis among all Clue-Implications, the Implication list is formed first (with the Clue # and its implications).

Deducing implications of individual Clues is easy and won't take time.

Implication list of rest 12 Clues: Values from Left to right in Horizontal Bonds are in actual Left to Right Positions:

Clue 1: With both Rani and Lipi facing in, Horizontal Bond: Rani-position-Lipi; Lipi not (Heritage, Desert, hill).

Clue 2: Monu/Lake/O.

Clue 5: With Lipi/I and Hal/O, Horizontal Bond: Lipi-position-position-position-Hal.

Clue 6: Rani either in 1 or 3 (rest of the implications assigned).

Clue 7: Gyan not (Hill, Heritage, Desert).

Clue 8: Epu/Heritage.

Clue 9: Desert-Gyan not neighbors.

Clue 10: Rani not Desert.

Clue 11: Hal/O.

Clue 12: Hal not Hill.

Clue 13: Horizontal Bond (two-directional): Beach/Hill-position-Hill/Beach.

Clue 16: With Monu/O and Epu/I, Horizontal Bond: Epu/Heritage-position-Monu/Lake: Two Vertical Bonds are separated by one position in a Horizontal Bond---promising.

Join the two Horizontal Bonds in Clue 1 first and Clue 5 second:

• Clue 1 + Clue 5 + Clue 6 Implications:
• Joined Horizontal Bond: Rani-position-Lipi-position-position-position-Hal (as Lipi is common in Clue 1 at rightmost position and in Clue 5 in leftmost positions of respective Horizontal Bonds).
• Rani either in 1 or 3.
• Lipi not (Heritage, Desert, hill).

Stage 4: Discovering the Breakthrough by Horizontal Bond Conflict

Previous stage assignment status shown for convenience of analysis.

The key to the breakthrough: The joined Horizontal Bond "Rani-position-Lipi-position-position-position-Hal" with Rani in either 1 or 3.

• First probable combination: Rani in 1, Lipi in 3, Hal in 7.
• Try to fit second most promising mixed Vertical-Horizontal Bond: "Epu/Heritage-position-Monu/Lake":
  • Epu cannot be in 5 as 7 for Monu occupied in this combination by Hal.
  • Epu cannot also be in 8 or 9 as 1 and 2 for Monu are already occupied in this combination.
• Conclusion: Epu/Heritage-position-Monu/Lake cannot be placed in this combination. The probable combination with Rani in 1 is invalid. Valid is Rani in 3.

Assignments with Rani in 3:

• Rani/I in 3, Lipi/I in 5, Hal/O in 9.
• Epu/Heritage/I in 8, Monu/Lake/O in 1 (position 9 adjacent to position 1 in circular seating).
• Gyan/I in 7 by default (Gyan only Person left and position 7 only free position remaining)
• Places liked left: Hill, Beach, River, Desert.

Stage 4 assignments (assignments are stopped here to show how Places liked are resolved):

Stage 5: Resolving Positions of Persons Liking Four Places Left: Horizontal Bond fitting and Places Disliked

Places disliked with Places left Hill, Beach, Desert, River:

• Lipi (5) not (Heritage, Desert, hill) by Clue 1
• Gyan (7) not (Hill, Heritage, Desert) by Clue 7.
• Rani (3) not Desert by Clue 10.

Assignment by common disliked place:

• Fiji in 2 gets Desert by default as the other three candidates without Places doesn't like Desert.
• Fiji/Desert in 2 is forced as Rani (3), Lipi (5), and Gyan (7) exclude Desert (Clues 1, 7, 10).
• Places left: Hill, Beach, River.

Clue 13: Horizontal Bond (two-directional): "Beach/Hill-position-Hill/Beach":

• Two probable combinations:
• "Beach/Hill(3)-position-Hill/Beach(5)", or,
• "Beach/Hill(5)-position-Hill/Beach(7)": Invalid as both Lipi in 5 and Gyan in 7 dislike Hill.
• Final assignments:
• Rani/Hill in 3, Lipi/Beach in 5.
• Gyan/River in 7 by default.

Completed assignments:

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Answers to the questions

Question 1. Who is sitting second to the right of Bree?

1. Monu
2. Cini
3. Rani
4. Gyan
5. Fiji

Answer 1. Option 5: Fiji.

Question 2. The person on the second right of Lipi likes to travel to,

1. Desert
2. Hill
3. River
4. Beach
5. Lake

Answer 2. Option 3: River.

Question 3. Which of the following combinations is correct?

1. Fiji-Hill-Facing away
2. Bree-Forest-Facing in
3. Rani-Lake-Facing away
4. Epu-Heritage-Facing in
5. Hal-Desert-Facing away

Answer 3. Option 4: Epu-Heritage-Facing in.

Question 4. Who among the following is an immediate neighbor of the one who likes Heritage?

1. The one who likes Temple
2. The one who likes Forest
3. Hal
4. Both 1 and 3
5. Fiji

Answer 4. Option 4: Both 1 and 3.

Question 5. Who among the following sits third to left of the person who likes Lake?

1. The one who likes Hill
2. Cini
3. Bree
4. Epu
5. The one who likes Desert

Answer 5. Option 3. Bree.

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Comments

• Circular seating puzzle assignment first principle: A suitable first assignment of a Person to a position anchors the end-joined linear assignment table with nine positions (position 1 adjacent and to the left of position 9). Subsequent assignment positions are relative to the first assignment position.
• Finding facing direction most important: Before taking up Clue analysis in depth, the decision to find all facing directions simplified further analysis.
• Formation of Implication list: The Clues being intricately interlinked (like a spaghetti), the list of terse but precise implications with Clue # identification made further analysis much easier.
• Critical breakthrough by joining of Horizontal Bonds: Two horizontal end-value shared bonds are joined to form a powerful long bond. This helped provide the critical breakthrough.
• Value of a mixed horizontal and vertical bond: Final resolution of Places liked could be achieved by the rare mixed types bond.

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

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