Question

If the yellow flags are flown on poles 2 and 4, which of the following must be true?

• A. \( \text{The white flags are flown on poles that are next to each other.} \)
• B. \( \text{a green flag is flown on pole that is next to two poles on which white flags are flown.} \)
• C. \( \text{A white flag is flown on a pole that is next to a pole on which a green flag is flown, and also next to a pole on which a yellow flag is flown.} \)
• D. \( \text{Each green flag is flown on a pole that is next to a pole on which a white flag is flown.} \)
• E. \( \text{Each yellow flag is flown on a pole that is next to a pole on which a green flag is flown.} \)

Hint:

Ensure adjacency and placement constraints.

Answer 1

The Correct Option is C

Step 1: Yellow on 2 and 4, 3 greens, 2 whites remain for 1, 3, 5, 6, 7; no green on 3.
Step 2: 3 must be white or yellow, but 5 no yellow, so 3W, 5G, 1G, 6W, 7G works; 1 next to 2Y, 3 next to 2Y and 4Y.
Step 3: 3W next to 2Y and 4Y, needs green nearby; 1G or 5G satisfies, always true.
Step 4: (C) must hold (e.g., 3W next to 2Y, 4Y, and 1G or 5G); others variable (A: 3W, 6W not adjacent; B: depends on placement; D/E: not always).