Four teams - Red (R), Blue (B), Green (G), and Yellow (Y) are competing in the final four rounds of the Inter-School Science Olympiad, labeled Round A, Round B, Round C, and Round D. Each round consists of one match between two teams, and every team plays exactly two matches. No team plays the same opponent more than once. The final schedule must adhere to the following rules:

• Rule 1 (Consecutive Play): The Green team (G) must play their two matches in consecutive rounds.
• Rule 2 (Fixed Appearance): The Yellow team (Y) must play in Round B.
• Rule 3 (Positional Constraint): The Red team (R) must play against the Blue team (B) in a round that is immediately before a round in which neither R nor B is playing.
• Rule 4 (Timing): The Blue team’s (B) first match must occur in an earlier round than the Green team’s (G) first match.
• Rule 5 (Opponent Link): The team that plays against the Red team (R) in the round that is not against the Blue team (B), is the same team that plays in Round D.

Finding the Match in Round C. What is the match scheduled for Round C?

The correct option is Green vs. Blue.

Let's analyze the given rules step-by-step to deduce the complete schedule for all four rounds: Round A, Round B, Round C, and Round D.

Given Information:

• 4 teams: Red (R), Blue (B), Green (G), and Yellow (Y).
• 4 rounds: Round A, Round B, Round C, Round D.
• Each round has 1 match between 2 teams, totaling 4 matches.
• Every team plays exactly 2 matches.
• No team plays the same opponent more than once.

Deduction Steps:

1. Rule 3 & Rule 1 Constraints:
Rule 3 states: The Red team (R) plays against the Blue team (B) in a round that is immediately before a round in which neither R nor B plays.
This means R vs. B must be in Round A, B, or C (since it must have a round immediately following it).
Furthermore, in the round immediately following R vs. B, neither R nor B plays. Since every match consists of 2 teams out of {R, B, G, Y}, if neither R nor B plays in that following round, the match in that round MUST be between the remaining two teams: Green (G) vs. Yellow (Y).

2. Rule 1 (Consecutive Play for G):
The Green team (G) plays their 2 matches in consecutive rounds.
Since one of G's matches is G vs. Y (which occurs right after R vs. B), G's other match must occur either immediately before or immediately after G vs. Y.

3. Rule 4 (Timing):
The Blue team’s (B) first match occurs in an earlier round than the Green team’s (G) first match.
Since R vs. B contains Blue's first match, R vs. B must happen BEFORE G's first match.
This implies R vs. B must be scheduled in Round A.

4. Determining Rounds for R vs. B and G vs. Y:
• Round A must be Red vs. Blue (R vs. B).
• Since G vs. Y occurs immediately after R vs. B, Round B must be Green vs. Yellow (G vs. Y).

5. Rule 2 Check:
Rule 2 states: The Yellow team (Y) must play in Round B. This matches our assignment of G vs. Y in Round B.

6. Determining Rounds C and D:
• Since G plays in consecutive rounds (Rule 1) and G's first match is in Round B, G's second match MUST be in Round C.
• The teams that still need to play their second matches are G, B, R, and Y.
• Rule 5 states: The team that plays against Red (R) in the round that is not against Blue (B) is the same team that plays in Round D.
This means Red plays in Round D! Therefore, Red's second match is in Round D.
Since Red plays in Round D, Red cannot play in Round C.
Thus, the match in Round C must involve Green (G) and Blue (B), i.e., Green vs. Blue.
• Consequently, Round D must feature the remaining second matches of Red (R) and Yellow (Y), i.e., Red vs. Yellow.

Complete Schedule Summary:
• Round A: Red vs. Blue
• Round B: Green vs. Yellow
• Round C: Green vs. Blue
• Round D: Red vs. Yellow

Therefore, the match scheduled for Round C is Green vs. Blue.