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Zorluk: OrtaSeating Arrangement

Six startup founders—Alice, Bob, Charlie, Diana, Ethan, and Fiona—are sitting in a straight row facing the audience during a panel discussion. The seats are numbered 1 to 6 from left to right.

Based on the following conditions, arrange the founders in the correct order from seat 1 (far left) to seat 6 (far right):
- Fiona is seated at one of the extreme ends of the row.
- Charlie sits exactly halfway between Alice and Fiona.
- Alice is seated third to the left of Diana.
- Bob is seated immediately next to Ethan.
- Ethan does not sit next to Diana.

Arrange the founders in their correct seating order from left to right.

  1. 1Fiona
  2. 2Charlie
  3. 3Alice
  4. 4Ethan
  5. 5Bob
  6. 6Diana

Cevap

The correct order from seat 1 to seat 6 is Fiona, Charlie, Alice, Ethan, Bob, and Diana.
The sequence must satisfy all constraints simultaneously. Fiona at an extreme end with Charlie halfway between her and Alice forces them into seats 1, 2, and 3. Alice being third to the left of Diana safely places Diana at seat 6. Finally, Ethan and Bob occupy seats 4 and 5, with Ethan at 4 to avoid sitting next to Diana.

Adım Adım Çözüm

1
Determine the possible positions for Fiona, Charlie, and Alice.
Fiona is at seat 1, Charlie at seat 2, and Alice at seat 3.
Fiona is at an extreme end (1 or 6). If Fiona is at 6 and Charlie is halfway between her and Alice, they could occupy 6, 5, 4 (F, C, A) or 6, 4, 2 (F, C, A). If Alice is at 4, Diana must be at 7 (4+3=7), which is impossible. If Alice is at 2, Diana is at 5, leaving seats 1 and 3 empty. Bob and Ethan must be adjacent, but seats 1 and 3 are separated. Thus, Fiona must be at seat 1, forcing Charlie to seat 2 and Alice to seat 3.
2
Determine Diana's position based on Alice.
Diana is at seat 6.
Alice is at seat 3. Since Alice is third to the left of Diana, Diana must be placed three seats to the right of Alice (3 + 3 = 6).
3
Place Ethan and Bob in the remaining seats.
Ethan is at seat 4 and Bob is at seat 5.
The only remaining empty seats are 4 and 5. Bob and Ethan must sit together. Since Ethan cannot sit next to Diana (who is at seat 6), Ethan cannot be at seat 5. Therefore, Ethan must sit at seat 4, leaving seat 5 for Bob.

Anahtar Kavram

Linear seating arrangement with relative positioning and exclusion criteria
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Konular

Seating Arrangement

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