Directions (1 to 3): A commercial flower grower raises flowers in each of the…
2025
Directions (1 to 3): A commercial flower grower raises flowers in each of the three growing seasons every year-spring, summer, and winter-with the year beginning in spring. Exactly seven different kinds of flowers- A, B, C, D, E, F, and G-are grown every year. Each kind of flower is grown at least once a year. The flowers are grown according to the following rules:
B can be grown in a growing season only if A is grown in the preceding season.
No more than three different kinds of flowers are grown in any one growing season.
No kind of flower can be grown in two seasons in a row.
A can be grown neither in the winter season nor in the same growing season as E or F.
C and D are always grown in the same growing season.
Which of the following is an acceptable schedule for the three growing seasons?
Schedule | Spring | Summer | Winter |
|---|---|---|---|
(a) | A | C, D, B | A, F, G |
(b) | C, F | A, D, G | B, E |
(c) | E, F | A | G, C, D, B |
(d) | A, C, D | B, E, F | G |
- A.
A
- B.
B
- C.
C
- D.
D
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept: In a rule-based scheduling puzzle, every stated constraint immediately rules out any candidate arrangement that violates it; the one candidate that survives every rule at once is the unique acceptable schedule. So the method is to test each rule against every candidate in turn, not to guess.
The rule that A can never be grown in Winter eliminates the schedule Spring: A; Summer: C, D, B; Winter: A, F, G — it grows A again in Winter.
The rule that C and D must always share the same growing season eliminates the schedule Spring: C, F; Summer: A, D, G; Winter: B, E — it grows C in Spring but D in Summer.
The rule limiting any one season to at most three kinds of flowers eliminates the schedule Spring: E, F; Summer: A; Winter: G, C, D, B — Winter carries four kinds.
The remaining schedule — Spring: A, C, D; Summer: B, E, F; Winter: G — satisfies every rule: A stays out of Winter and is never with E or F (they fall in Summer); C and D sit together in Spring; no season exceeds three kinds; B (Summer) correctly follows A (Spring); no kind repeats in two consecutive seasons; and all seven kinds A through G are each grown exactly once across the year.
Cross-check: Six independent rules were each tested against all four candidates, and exactly one schedule — Spring: A, C, D; Summer: B, E, F; Winter: G — violates none of them while placing every one of the seven flower kinds. That confirms it as the unique acceptable schedule.