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Difficulty: Very hardSeating Arrangement

Six friends—Paul, Quinn, Riley, Sam, Tara, and Uma—are seated in a straight line extending from West to East. Some of them are facing North, while others are facing South. Each person is wearing a different colored shirt: Red, Blue, Green, Yellow, White, and Black.

The seating arrangement is governed by the following conditions:
1. Paul sits third from the western end and faces North.
2. Only two people sit between Paul and the person wearing a Black shirt.
3. Uma wears a Black shirt.
4. Sam sits second to the left of Uma.
5. Riley sits to the immediate right of Sam.
6. Tara sits to the immediate left of Paul.
7. The person wearing a Blue shirt sits to the immediate right of Tara.
8. Quinn wears a Blue shirt.
9. The persons sitting at the extreme ends face the same direction.
10. The person wearing a Yellow shirt sits third to the right of Quinn.
11. The person wearing a Green shirt is an immediate neighbor of Tara.
12. Riley does not wear a Red shirt.
13. Sam and Riley face opposite directions.

Based on these conditions, match each person to the color of the shirt they are wearing.

  • QuinnBlue shirt
  • TaraRed shirt
  • PaulGreen shirt
  • SamYellow shirt
  • RileyWhite shirt

Answer

Quinn matches with Blue, Tara with Red, Paul with Green, Sam with Yellow, and Riley with White.
The puzzle is solved deterministically by anchoring Paul at Position 3. This forces Uma to Position 6. To satisfy relative positions, Uma must face North (putting Sam at 4) and Sam must face North (putting Riley at 5). Tara is at 2. Since Quinn wears Blue, Tara must face South so Quinn can sit to her immediate right at Position 1. Quinn faces North (matching Uma at the other end), making Sam the person third to his right (Yellow). Tara's Green neighbor must be Paul. Finally, between Tara and Riley, Riley cannot be Red, so Riley is White and Tara is Red.

Step-by-Step Solution

1
Determine the anchoring positions of Paul, Uma, and Sam.
Paul is at Position 3 (facing North). Uma is at Position 6 (Black). Sam is at Position 4 (facing North).
Paul is 3rd from West. Two people between Paul (3) and Black means Black is at 6 (Uma). For Sam to be second to Uma's left on the bench, Uma must face North, placing Sam at Position 4.
2
Determine the positions of Riley and Tara.
Riley is at Position 5 (facing South). Tara is at Position 2.
Riley is immediate right of Sam. If Sam faced South, right would be 3 (Paul). So Sam faces North, placing Riley at 5. Tara is immediate left of Paul (who faces North), placing Tara at 2. Sam and Riley face opposite directions, so Riley faces South.
3
Deduce Quinn's position and Tara's facing direction.
Quinn is at Position 1 (Blue), and Tara faces South.
Blue is immediate right of Tara. If Tara faced North, her right would be 3 (Paul). But Quinn wears Blue, so Paul can't be Blue. Tara must face South, making her right Position 1, which is occupied by Quinn (Blue).
4
Assign the remaining colors based on directional conditions.
Sam is Yellow, Paul is Green, Tara is Red, Riley is White.
Extreme ends face the same direction, so Quinn (1) faces North like Uma (6). Third to Quinn's right is Sam (4), so Sam is Yellow. Tara's neighbor with Green must be Paul. Riley isn't Red, so Riley is White, leaving Red for Tara.

Key Concept

Simultaneous deduction of linear positions and facing directions using relative placement constraints and process of elimination.
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Topics

Seating Arrangement

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