Directions (1 to 3): A commercial flower grower raises flowers in each of the…
2024
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 grew 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. Question 1: If G is grown in the spring and E in the summer of one year, then which of the following can also be grown in the summer?
- A.
F
- B.
A
- C.
C
- D.
D
Attempted by 1 students.
Show answer & explanation
Correct answer: A
In season-assignment logic puzzles, work forward from the rule that most tightly restricts one variable. Once a placement rule eliminates every season but one for that variable, its season is fixed, and any conditional rule written in terms of it ("X is allowed only if Y holds in the preceding season") can then be resolved with certainty instead of guessed.
A cannot be grown in winter, and cannot share a season with E or F. Since E is fixed in summer here, A cannot be summer either, so spring is the only season left for A, and A must be grown there.
B is allowed in a season only if A is grown in the immediately preceding season. With A now fixed in spring, the only season satisfying this for B is summer, the season right after spring; winter would need A in summer, which is impossible, so B must be grown in summer.
Summer therefore already holds two flowers, E and B, before considering the answer choices.
C and D are always grown together in the same season, so choosing either one for summer forces both in, which would put four different flowers (E, B, C, D) in one season and break the rule that no more than three kinds may be grown in a season. So neither C nor D can join summer here.
F is not restricted from sharing a season with B or E; the only rule involving F is that A cannot share its season, and A is in spring, not summer. So F can validly occupy the one remaining slot in summer alongside E and B.
Spring | Summer | Winter |
|---|---|---|
G, A | E, B, F | C, D |
This full-year layout satisfies every rule: no season exceeds three flowers, A avoids winter and avoids sharing a season with E or F, B follows immediately after A's season, and C stays paired with D. F is confirmed as the flower that can also be grown in summer.