Question

If X is orange and Z is purple, an interchange of these colors between X and Z
requires a total of at least how many color changes?

• A. \( \text{Two} \)
• B. \( \text{Three} \)
• C. \( \text{Four} \)
• D. \( \text{Five} \)
• E. \( \text{Six} \)

Hint:

Count minimum transitions via intermediates.

Answer 1

The Correct Option is C

Step 1: X starts orange, Z starts purple; goal: X to purple, Z to orange, \( X \neq Z \).
Step 2: Valid changes: red to/from green, red to/from orange, red to/from purple,
purple to/from orange; one light changes at a time.
Step 3: X (orange) to purple needs red intermediate (orange to red to purple),
Z (purple) to orange needs red intermediate (purple to red to orange), total 4 changes.
Step 4: (C) four is the minimum.