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A farmer plants only five different kinds of vegetables - beans, corn, kale, peas, and squash. Every year the farmer plants exactly three kinds of vegetables according to the following restrictions: If the farmer plants com, the farmer also plants beans that year. If the farmer plants kale one year, the farmer does not plant it the next year. In any year, the farmer plants no more than one of the vegetables the farmer planted in the previous year.


If the farmer plants beans, corn, and kale in the first year, which of the following combinations must be planted in the third year?

(A) Beans, corn, and kale
(B) Beans, corn, and peas
(C) Beans, kale, and peas
(D) Beans, peas, and squash
(E) Kale, peas, and squash

ANSWER
First year: C, B, K
Second year:
- K cannot be planted. We are left with C, B, S, P - If the farmer plants kale one year, the farmer does not plant it the next year -
-
If the farmer plants corn, the farmer also plants beans that year
If C is planted => (C, B, S) (C, B, P) [1]
If C is not planted => (B, S, P) [2]
Third year:
- Case [1] does not work, because 2 of the plants (C, B) will appear. - no more than one of the vegetables the farmer planted in the previous year -
- In Case [2], only one of (B, S, P) can appear. Since the farmer grows 3 plants. The plants grown will have to be (x, C, K). Only answer A can satisfy (B, C, K)
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