Question

If the two yellow flags are flown on poles that are next to each other and the two white flags are flown on poles that are next to each other, then the flags flown on poles 2 and 6 must be

• A. \( \text{both green} \)
• B. \( \text{green and white, respectively} \)
• C. \( \text{white and green, respectively} \)
• D. \( \text{yellow and green, respectively} \)
• E. \( \text{yellow and white, respectively} \)

Hint:

Check adjacency and restrictions.

Answer 1

The Correct Option is B

Step 1: Yellow flags (2) must be adjacent, not on pole 5, so possible pairs are (1,2), (2,1), (4,6), (6,4), (6,7), (7,6).
Step 2: White flags (2) must be adjacent, so pairs like (1,2) conflict with yellow; try (4,5) or (6,7), but 5 is yellow-free, so (6,7) works if yellow elsewhere.
Step 3: Green flags (3) cannot be adjacent or on 3, so distribute remaining poles (1,3,5 if available) with constraints.
Step 4: If yellow on (4,6), white on (6,7) conflicts; try yellow on (1,2), white on (6,7), then 3 (no green), 4,5,7 used, 2 green on 4,5 conflicts; adjust: yellow (2,4), white (6,7), then 1,3,5 for green, but 3 no green, so 1 green, 5 green, 2 green conflicts; correct: yellow (1,2), white (6,7), 3 no green, 4 green, 5 green, but 4,5 adjacent green fails; final: yellow (2,4), white (6,7), 1 green, 3 no, 5 green, works; thus 2 green, 6 white.