A man has to plant exactly four varieties of flowers in a flower bed in his garden, one variety in each of the four rows, in an ascending order of height from the first row to the fourth row. The seven varieties available to the man, in ascending order of height, are red begonias (RB), pink petunias (PP), orange marigolds (OM), red geraniums (RG), white snapdragons (WS), yellow zinnias (YZ) and pink cosmos (PC). The following restrictions on color arrangements apply: No two varieties of the same color can be planted. Orange flowers cannot be planted in a row immediately adjacent to a row of yellow flowers. If the man plants the zinnias in the third row, then which of the following can be planted in the second row?
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Explanation: The arrangement is Row 1, Row 2, YZ, Row 4. Varieties must be in ascending order: RB, PP, OM, RG, WS, YZ, PC. YZ is in Row 3. Available for Row 1 and Row 2 (must be shorter than YZ) are {RB, PP, OM, RG, WS}. (1) No same color: YZ is Yellow, so no other Yellow. (2) OM not adjacent to YZ: OM cannot be in Row 2. (OM is Orange). Row 4 must be PC (taller than YZ). If PC is in Row 4, PP is excluded from Row 1 and Row 2 (Condition 1, Pink). Available for Row 1 and Row 2: {RB, OM, RG, WS}. Since OM is excluded from Row 2, the options for Row 2 are {RB, PP, RG, WS}. Now, let's re-evaluate based on the options. If the man plants YZ in the third row, then Row 4 must be PC (as it is the only one taller than YZ). PC is Pink, so PP is excluded. YZ is Yellow, so OM is excluded from Row 2. The available flowers for Row 1 & 2 (shorter than YZ) are {RB, PP, OM, RG, WS}. Excluding OM (from Row 2) and PP: {RB, RG, WS}. Row 2 options are {RG, WS}. RG is Red, so RB is excluded. If Row 2 is RG, Row 1 must be RB (but RB is excluded). If Row 2 is WS, Row 1 can be {RB, PP, OM, RG}. If Row 4 is PC (Pink), then PP is excluded. Row 3 is YZ (Yellow), so OM is excluded from Row 2. Let's check the options for Row 2, assuming a valid overall arrangement exists. (A) Begonias (RB) in Row 2: Row 1 must be empty (nothing shorter than RB). Not possible. (B) Petunias (PP) in Row 2: Row 1 must be RB (only shorter option). {RB, PP, YZ, PC} is valid. RB/RG is ok. PP/PC is excluded. YZ not next to OM is ok. So PP can be in Row 2. (C) Marigolds (OM) in Row 2: OM is adjacent to YZ. Not allowed. (D) Geraniums (RG) in Row 2: Row 1 must be RB or PP or OM. If Row 1 is RB, RG is excluded. If Row 1 is PP, Row 4 (PC) is excluded. If Row 1 is OM, not allowed next to YZ. Not possible. (E) Cosmos (PC) in Row 2: PC is taller than YZ, so not allowed. The only valid option is B. (The source provides no correct option, but B is logically possible).