8 Person 8 Preference Circular Seating Reasoning Puzzle

8 Persons like 8 icecreams and sit around a circular table. A few face inward and others face away from center. Solve to answer 5 questions from 12 Clues.

8 Person with 8 Icecream Preference Circular Seating Reasoning Puzzle

Description:

Eight persons namely A, B, C, D, E, F, G and H sit around a circular table facing towards or away from the center. Each of them likes a different icecream flavor, one of the flavors being Strawberry.

The following is what we know about them.

Clues:

1. H's neighbors face in same direction but opposite to that of H.
2. G sits third to the left of E who faces towards the center.
3. D's spouse who likes Chocolate flavor sits third to the left of D.
4. C sits third to the right of a man and they face in the same direction.
5. B's immediate neighbors face in same direction but opposite to that of B.
6. The woman who likes Vanilla flavor sits opposite to the man who likes Red Velvet.
7. A who likes Black Currant flavor sits second to the left of D and they face in the same direction.
8. The immediate neighbors of C like Vanilla and Mulberry flavors.
9. B and F sit together and none of them sits with A and D.
10. G's spouse who likes Fruit n Nut flavor sits second to the left of G.
11. The immediate neighbors of H's only sister who is neither C nor E are A and D.
12. B who likes Butter Scotch flavor is the only one whose both immediate neighbors are of opposite gender to B.

Questions

Question 1. How many persons face away from the center?

1. 6
2. 4
3. 5
4. 3
5. Cannot be determined

Question 2. How many men are there?

1. 3
2. 6
3. 5
4. 4
5. Cannot be determined

Question 3. Who likes Strawberry flavor?

1. G
2. E
3. F
4. H
5. Cannot be determined

Question 4. Who sits second to the left of C?

1. A woman
2. The one who likes Fruit N Nut
3. G
4. Both options 1 and 3
5. Options 1, 2 and 3

Question 5. Who sits opposite to the one who likes Mulberry?

1. The one who likes Strawberry
2. C
3. A
4. H
5. None of these

Hints:

• Design the convenient assignment table.
• Make the first assignment with facing directions to anchor the assignment table grid. Affect maximum number of positions.
• Use Clues referring to assigned values. Form and use two-position blocks for breakthroughs.
• Use neighbor constraints of facing directions for breakthroughs.
• Use opposite sitting Clue for breakthrough.

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Solution to 8 Person with 8 Icecream Preference Circular Seating Reasoning Puzzle (SBI PO)

The circular table with 8 Persons sitting in 8 positions:

8 Persons sit in 8 positions from 1 to 8 with position 8 adjacent to position 1. To make assignments of Persons, Icecream flavors liked, Facing directions and Gender of Persons to the correct positions convenient, the circular table is split at the junction of positions 1 and 8 and flattened to a linear assignment table (with positions 1 and 8 considered as adjacent):

Assignment table to be used:

Stage 1: First Assignments by Two-position Block affecting maximum number of positions: Anchoring the Grid

Clue 9. B and F sit together and none of them sits with A and D.

• Two-position Block: B/F-F/B placed in 2 and 3; 1/not A,D; 4/not A,D
• Four positions affected simultaneously.

Stage 1 assignments:

Stage 2: Link reference to A, D - Elimination by Logical Analysis and Two-position Block

Clue 11. The immediate neighbors of H's only sister who is neither C nor E are A and D.

• G is H's sister by elimination and is a Woman (either B or F cannot have immediate neighbors A and D and H's sister is not C or E → only G is left to be H's sister).
• G can either be in 6 or 7 with A and D in adjacent neighboring positions.

Clue 2. G sits third to the left of E who faces towards the center.

• If G in 7, E won't have any place to occupy as it requires blocked position 2 for G to be on its third left.
• G cannot be in 7 → E/I in 1, G/W in 6, A/D in 5, D/A in 7 → Two-position block.

Clue 7. A who likes Black Currant flavor sits second to the left of D and they face in the same direction.

• A/Black Currant/I in 5 (D/I in 7) or A/Black Currant/O in 7 (D/O in 5).

Stage 2 assignments:

Stage 3: Two-position Blocks, Relations Revealed by Logical Reasoning

Clue 3. D's spouse who likes Chocolate flavor sits third to the left of D.

• Chocolate/(D's spouse) in 4 or 8.

Clue 10. G's spouse who likes Fruit n Nut flavor sits second to the left of G.

• Fruit N Nut/(G's spouse) in 8 or 4.
• Clues 3 and 10 form a two-position Block of positions 4 and 8 by Chocolate/(D's Spouse) or Fruit N Nut/(G's spouse)

Logic identifying D's spouse and G's spouse:

• C and H are left for positions 4 and 8.
• As G is H's sister, C is G's spouse and H is D's spouse.
• Two-position block of H/C (Chocolate/Fruit N Nut)-C/H (Fruit N Nut/Chocolate) in 4 and 8.

Stage 3 assignments:

Stage 4: Critical Breakthrough by Facing Directions in Adjacent Positions

Identifying whether C or H is in 8: Critical breakthrough:

Clue 8. The immediate neighbors of C like Vanilla and Mulberry flavors.

• With C in 4, positions 3 and 5 are blocked by Vanilla/Mulberry.
• With C in 8, positions 7 and 1 are blocked by Vanilla/Mulberry.

Clue 1. H's neighbors face in same direction but opposite to that of H.

• If C in 4, H in 8 → Its neighbors are A/7/O and E/1/I → O in 7 violates Clue 1.
• C in 4 and H in 8 invalid.
• Valid: C in 8, H in 4.

Critical breakthrough assignments:

• C/Fruit N Nut in 8, H/Chocolate in 4.
• Immediate neighbors of C: D/(Vanilla/Mulberry)/I in 7, E/(Mulberry/Vanilla)/I in 1.
• A/Black Currant/I in 5 (with Vanilla/Mulberry block in 7 A/Black Currant cannot be in 7).
• A and D both face inward by Clue 7.
• Being G's spouse, C is a man M.

Stage 4 assignments:

Stage 5: Resolving Gender and Facing Directions: Use of Opposite Sitting

Clue 4. C sits third to the right of a man and they face in the same direction.

• A/M/I in 5, C/I in 8.

Clue 1. H's neighbors face in same direction but opposite to that of H.

• H/O in 4, Facing I in 3.

Clue 6. The woman who likes Vanilla flavor sits opposite to the man who likes Red Velvet.

• For Vanilla in 1, opposite position 5 taken → D/Vanilla/W in 7, Red Velvet/M in opposite position 3, Mulberry in 1.
• Being D's spouse, H in 4 is a man M.

Clue 12. B who likes Butter Scotch flavor is the only one whose both immediate neighbors are of opposite gender to B.

• B/Butter Scotch/W in 2, E/M in 1, Strawberry in 6 by default.
• With B in 2, F in 3.

Clue 5. B's immediate neighbors face in same direction but opposite to that of B.

• B/O in 2, F/I in 3.

G's Facing direction: As C, G's spouse is in 8 sitting second left of G by Clue 10, G/O in 6.

Assignments completed:

Assignments in vertical table form:

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Key Deductions:

• Clue 9: "B and F sit together but not with A or D" → Block B/F-F-B in 2 and 3, "not A or D" in 1 and 4.
• Clues 11 + 2 + 7: G/W is H's sister in only available 6, as G sits third left of E in 1. A(Black Currant)/D, and D/A(Black Currant) in 5 and 7. A and D have same facing directions.
• Clues 3 + 10: (C, G's spouse/Fruit N Nut)/(H, D's spouse/Chocolate) form a two-position block in 4 and 8.
• Clues 8 + 1: Critical breakthrough: H in 4 and C in 8 identified as valid by facing direction conflict of immediate neighbors of H, if it were on 8.
• Clues 4 + 1 + 6 + 12 + 5 includes opposite sitting Clue 6: provided rest of the assignments.

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Answers:

1. Q1. Option 4: Three (B in 2, H in 4 and G in 6 face away from the center).
2. Q2. Option 3: Five (E, F, H, A and C are men).
3. Q3. Option 1: G (G likes Strawberry).
4. Q4. Option 4: Both options 1 and 3 (G sitting second left of C is a woman).
5. Q5. Option 3: A (E in 1 likes Mulberry and on its opposite position 5 sits A).

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Comments

The important strategies and use patterns inherent in the Clues that ensured a seamless efficient solutions:

• Anchor First Assignment: Maximum positions affected by Clue 9: The two value block of B/F in 2 and 3 is as good as assigning values to the two positions (as no other person can be assigned to the positions). Additionally, access of A/D are restricted for positions 1 and 4 at the same time.
• Link reference and Two-position Block: Clues 11 + 2 + 6 provided the assignments by referring at already assigned A, D, elimination by logic analysis and two-position block.
• Breakthrough by two-position block: Clues 3 + 10 provided the breakthroughs by two-position block.
• Critical breakthrough by Facing direction constraints on adjacent positions by Clues 8 + 1.

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

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