Question

Which of the following, CANNOT be true?

• A. \( \text{Green flags are flown on poles 1 and 4.} \)
• B. \( \text{White flags are flown on poles 1 and 7.} \)
• C. \( \text{Yellow flags are flown on poles 1 and 7.} \)
• D. \( \text{A green flag is flown on pole 1 and a yellow flag is flown on pole 7.} \)
• E. \( \text{a white flag is flown on pole 1 and a yellow flag is flown on pole 7.} \)

Hint:

Check adjacency and pole 3 restriction.

Answer 1

The Correct Option is A

Step 1: No two green flags can be adjacent, and none on pole 3; poles 1 and 4 are adjacent to 2 and 3/5.
Step 2: Green on 1 and 4 violates adjacency rule since 1 and 4 are separated by 2,3, but 4 is next to 3 (no green on 3), and 1 next to 2 must avoid green adjacency.
Step 3: Other poles (e.g., 5,6,7) for remaining greens must avoid 3 and adjacency, but 1 and 4 green fails (e.g., 2,3,5 need filling, 4 green next to 5 green possible only if 3 not green).
Step 4: Configuration with 1G, 4G impossible (e.g., 2W, 3W, 5G, 6Y, 7Y has 1,4 adjacent green issue); thus (A) cannot be true.