Seven persons — A, B, C, D, E, F, and G — live in a seven-floor building numbered from 1 (ground floor) to 7 (top floor). Each person likes a different color: Green, Red, Violet, Purple, Black, Pink, and White. The following conditions apply:

- G lives on an even-numbered floor and is three floors above the person who likes Black.
- The number of persons living above the one who likes Purple equals the number of persons living below the one who likes Black.
- C lives two floors above the person who likes White, who lives on an odd-numbered floor.
- C does not like Black.
- B lives two floors above the person who likes Violet.
- The person who likes Green lives just above the one who likes Pink.
- More than three persons live between E and F, and F lives just above D.

Which of the following statements is true?

I. G does not live on a prime-numbered floor.

II. A lives above the person who likes Red.

III. There is at least a two-floor gap between G and F.

Question

Seven persons — A, B, C, D, E, F, and G — live in a seven-floor building numbered from 1 (ground floor) to 7 (top floor). Each person likes a different color: Green, Red, Violet, Purple, Black, Pink, and White. The following conditions apply:

- G lives on an even-numbered floor and is three floors above the person who likes Black.
- The number of persons living above the one who likes Purple equals the number of persons living below the one who likes Black.
- C lives two floors above the person who likes White, who lives on an odd-numbered floor.
- C does not like Black.
- B lives two floors above the person who likes Violet.
- The person who likes Green lives just above the one who likes Pink.
- More than three persons live between E and F, and F lives just above D.

Which of the following statements is true?

I. G does not live on a prime-numbered floor.

II. A lives above the person who likes Red.

III. There is at least a two-floor gap between G and F.

Accepted Answer

**Solution:**

1. From the condition that G lives on an even floor and is three floors above the person who likes Black, and since the building has 7 floors, Black must be on floor 1 and G on floor 4.

2. The number of people above Purple equals the number below Black. Since Black is on floor 1, below Black is zero persons. Therefore, Purple must be on the top floor (floor 7) so that no one is above Purple.

3. C lives two floors above the person who likes White, and White lives on an odd floor. Possible odd floors for White are 1, 3, 5, or 7. Since floor 7 is taken by Purple, and floor 1 by Black, White must be on floor 3, so C is on floor 5.

4. C does not like Black, so C's color is not Black.

5. B lives two floors above the person who likes Violet. Since G is on floor 4 and likes Violet (to satisfy B's position), B must be on floor 6.

6. The person who likes Green lives just above the one who likes Pink. Since B is on floor 6 and likes Green, Pink must be on floor 5, which matches C's floor.

7. More than three persons live between E and F, and F lives just above D. The only way to satisfy this is E on floor 7 and F on floor 2, D on floor 1.

8. Assigning remaining colors and persons:
   - Floor 7: E - Purple
   - Floor 6: B - Green
   - Floor 5: C - Pink
   - Floor 4: G - Violet
   - Floor 3: A - White
   - Floor 2: F - Red
   - Floor 1: D - Black

**Check statements:**

- I. G is on floor 4, which is not a prime number — True.
- II. A (floor 3) lives above F (floor 2) who likes Red — True.
- III. G (floor 4) and F (floor 2) have only one floor between them (floor 3), so the gap is 1 floor, not at least 2 — False.

**Answer:** Both I and II are true.

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