Circular Seating Arrangement Puzzle Analysis

Start by carefully reading and understanding all the given clues about the eight friends— A, B, C, D, E, F, G and H— sitting around a circular table facing the centre, and the television brands they like—Onida, Sony, Samsung, Micromax, TCL, LG, Toshiba and Sansui.

Key Clues Extracted

• A sits third to the right of the person who likes Sansui.
• A does not like Samsung.
• E is not an immediate neighbour of H.
• C sits on the immediate right of the person who likes Samsung.
• Neither A nor H likes TCL or Sony.
• The person who likes TCL is not an immediate neighbour of the person who likes Sansui.
• The person who likes Onida sits second to the left of E.
• The person who likes Onida is an immediate neighbour of the both persons who like LG and Toshiba.
• Person who likes Toshiba sits third to the right of B.
• B does not like TCL.
• F is not an immediate neighbour of A.
• G is not an immediate neighbour of the person who likes Onida.
• Only two people sit between the person who likes Toshiba and H.
• The persons who like TCL and the Sony are immediate neighbours of each other.

Step-by-Step Deduction Process

We will use a process of deduction, combining clues to build the seating arrangement and brand preferences. Let's number the positions 1 through 8 around the table in a clockwise direction, assuming 'right' is clockwise.

Placing Key Individuals and Brands

From the question, we need to find the brand liked by H. Let's start by exploring possibilities involving H and key brands mentioned in relation to H.

From Clue 4: C sits on the immediate right of the person who likes Samsung. Let P(Samsung) denote the person who likes Samsung. So, P(Samsung) → C (right, i.e., clockwise).

From Clue 13: Only two people sit between the person who likes Toshiba and H. In an 8-person circle, this means they are 3 positions apart.

Let's try assuming H likes Samsung, as this is the nature of the question we need to answer. If H likes Samsung, then P(Samsung) is H. From Clue 4, C sits immediately right of H.

Let's place H at Position 7 for now.

• Position 7: H (Likes Samsung)

Immediate right of H (Position 7) is Position 8. So, C is at Position 8.

• Position 8: C

From Clue 13: Two people between P(Toshiba) and H (Position 7). This means P(Toshiba) is 3 positions away from Position 7. Going right (clockwise), Position 7 + 3 = Position 10, which is Position 2 in an 8-person circle. Going left (anti-clockwise), Position 7 - 3 = Position 4. So, the person liking Toshiba is at Position 2 or Position 4.

From Clue 9: Person who likes Toshiba sits third to the right of B. This means B is third to the left of the person liking Toshiba.

• If P(Toshiba) is at Position 2, B is third left of Position 2 (2 → 1 → 8 → 7). B is at Position 7. But Position 7 is H. This is a contradiction.
• If P(Toshiba) is at Position 4, B is third left of Position 4 (4 → 3 → 2 → 1). B is at Position 1. This is possible.

So, the person liking Toshiba is at Position 4, and B is at Position 1.

• Position 1: B
• Position 4: Person liking Toshiba

Current partial arrangement:

From Clue 8: The person who likes Onida is an immediate neighbour of the persons liking LG and Toshiba. Person liking Toshiba is at Position 4. So, the person liking Onida must be at Position 3 or Position 5.

From Clue 7: The person who likes Onida sits second to the left of E. This means E sits second to the right of the person liking Onida.

• If P(Onida) is at Position 3, E is second right of Position 3 (3 → 4 → 5). E is at Position 5. This is possible.
• If P(Onida) is at Position 5, E is second right of Position 5 (5 → 6 → 7). E is at Position 7. But Position 7 is H. This is a contradiction.

So, the person liking Onida is at Position 3, and E is at Position 5.

• Position 3: Person liking Onida
• Position 5: E

From Clue 8: P(Onida) (Position 3) is neighbour of P(LG) and P(Toshiba) (Position 4). Since P(Toshiba) is at Position 4, the other neighbour of Position 3 liking LG must be at Position 2. So, the person liking LG is at Position 2.

• Position 2: Person liking LG

Current seating arrangement with known brands/people/positions:

People placed: B(P1), E(P5), H(P7), C(P8). People liking specific brands: P2(LG), P3(Onida), P4(Toshiba), P7(Samsung).

Remaining people for positions 2, 3, 4, 6 are A, D, F, G.

Person at P2 likes LG, Person at P3 likes Onida, Person at P4 likes Toshiba.

From Clue 12: G is not immediate neighbour of the person who likes Onida (Position 3). Neighbours of Position 3 are Position 2 and Position 4. So G is not at Position 2 or Position 4.

The people at Positions 2, 3, 4 are among A, D, F, G. Since G is not at P2 or P4, G must be at Position 3 or Position 6 (the only other unassigned spot from {A, D, F, G}). G cannot be at P3 as P3 is Person liking Onida, and G is not a neighbour of P3. Wait, the clue says G is not a neighbour, not that G is the person. G is not adjacent to the person at P3. This is already satisfied as Position 2 and 4 are neighbours of Position 3, and G is not at P2 or P4. The people who are G must be placed in the remaining spots {P2, P3, P4, P6}. Among these spots, P2 and P4 are neighbours of P3. So G cannot be at P2 or P4. The possible positions for G among {P2, P3, P4, P6} are P3 or P6. G cannot be the person at P3 (likes Onida). So G must be at Position 6.

• Position 6: G

The people at Positions 2, 3, 4 are now {A, D, F}. Person at P2 likes LG, Person at P3 likes Onida, Person at P4 likes Toshiba.

Remaining brands for Positions 1, 5, 6, 8 are Sansui, Sony, Micromax, TCL.

Brands liked by B(P1), E(P5), G(P6), C(P8) are {Sansui, Sony, Micromax, TCL}.

From Clue 5: Neither A nor H likes TCL or Sony. H at P7 likes Samsung. OK. A is at P2, P3, or P4. A != TCL, Sony.

From Clue 10: B does not like TCL. B is at P1. B != TCL.

From Clue 14: Persons who like TCL and Sony are immediate neighbours. The brands TCL and Sony must be liked by people at adjacent positions from {P1, P5, P6, P8}.

• P1 and P8 are neighbours. (B, C)
• P5 and P6 are neighbours. (E, G)

Possible (Brand TCL, Brand Sony) pairs for adjacent people: (B, C), (C, B), (E, G), (G, E).

• B likes TCL, C likes Sony. (Contradicts Clue 10: B != TCL)
• C likes TCL, B likes Sony. (Possible)
• E likes TCL, G likes Sony. (Contradicts Clue 5: E != TCL)
• G likes TCL, E likes Sony. (Possible)

So, either (C likes TCL and B likes Sony) OR (G likes TCL and E likes Sony).

Let's use Clue 10 (B != TCL) and Clue 5 (E != TCL). This means B and E cannot like TCL. The available people for TCL and Sony are B, C, E, G. So either C or G likes TCL, and the other neighbour (B, E) likes Sony.

The pairs of people available for TCL/Sony are (B, C) and (E, G). B cannot like TCL, E cannot like TCL. So C or G must like TCL. Their neighbour must like Sony.

• If C likes TCL, its neighbour B must like Sony. This is consistent with Clue 10.
• If G likes TCL, its neighbour E must like Sony. This is consistent with Clue 5.

So, we have two possibilities for the Sony/TCL pair:

1. B likes Sony, C likes TCL. (Brands for P1 & P8)
2. E likes Sony, G likes TCL. (Brands for P5 & P6)

Let's test possibility 2: E likes Sony (P5), G likes TCL (P6).

• Position 5: E (Sony)
• Position 6: G (TCL)

Remaining brands for B(P1) and C(P8) are {Sansui, Micromax}.

From Clue 1: A is 3rd right of the person liking Sansui. The person liking Sansui is B (P1) or C (P8).

• If B likes Sansui (P1), A is 3rd right of P1 (1 → 2 → 3 → 4). A is at Position 4.
• If C likes Sansui (P8), A is 3rd right of P8 (8 → 1 → 2 → 3). A is at Position 3.

A is one of the people at {P2, P3, P4}. These positions like {LG, Onida, Toshiba}.

• If A is at Position 4 (likes Toshiba), then the person liking Sansui must be at Position 1 (B). So B likes Sansui. This fits the case where B and C like Sansui/Micromax. If B likes Sansui, C likes Micromax.

Let's assume B likes Sansui (P1) and C likes Micromax (P8). Then A is at Position 4 (likes Toshiba).

• Position 1: B (Sansui)
• Position 4: A (Toshiba)
• Position 8: C (Micromax)

Current arrangement state:

People: A(P4), B(P1), C(P8), E(P5), G(P6), H(P7). Remaining people for P2, P3 are D, F.

Person at P2 likes LG, Person at P3 likes Onida. So {P2, P3} = {D, F}.

From Clue 11: F is not immediate neighbour of A (Position 4). Neighbours of A are Position 3 and Position 5. E is at P5. So F is not at Position 3 or Position 5. Since F is one of D, F at P2 or P3, F cannot be at P3. Thus F must be at Position 2 (likes LG). D must be at Position 3 (likes Onida).

Final Arrangement:

Let's verify this arrangement against all the clues. All clues are satisfied (as shown in the thought process). The person H is at Position 7 and likes Samsung.

Conclusion

Based on the step-by-step deduction and verification of all clues, the final arrangement of people and their preferred television brands is determined. The person H is sitting at Position 7 and likes the Samsung brand.

Revision Table: Key Clues & Interpretations

Additional Information: Circular Arrangement Concepts

Circular arrangement puzzles are common in logical reasoning sections of exams. Understanding the concepts of immediate left/right and positions "between" is crucial.

• Immediate Left/Right: In a circular arrangement facing the center, 'right' is typically interpreted as clockwise movement around the circle, and 'left' as anti-clockwise movement.
• ‘N’ People Between: If there are ‘N’ people sitting between two people, say P1 and P2, it means P1 and P2 are (N+1) positions away from each other along the circle in either direction. In an 8-person circle, 2 people between means a distance of 3 positions. If P1 is at position X, P2 is at position X+3 or X-3 (modulo 8, adjusting for circularity).
• Facing Center: When all individuals face the center, the left and right directions are consistent for everyone relative to their own position.
• Deduction Strategy: Start with the most restrictive clues or those that link multiple entities (people, brands, positions). Build partial arrangements and test subsequent clues against them. If a clue creates a contradiction, backtrack and try a different possibility.