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.

Assessing a Rule Violation If the match in Round D was (Blue vs. Yellow), which of the original rules would be violated by this schedule change?

The correct answer is Rule 5 (Opponent Link).

Step 1: Understand the Setup and Constraints
There are 4 rounds: Round A, Round B, Round C, and Round D.
There are 4 teams: Red (R), Blue (B), Green (G), and Yellow (Y).
Each round has 1 match between 2 teams. Total matches = 4.
Each team plays exactly 2 matches.
No team plays the same opponent twice.
We are given that in Round D, the match is Blue vs. Yellow (B vs Y).

Step 2: Determine the remaining match participants
Since Round D is (B vs Y), the teams playing in Round D are B and Y.
Team Y plays in Round B (Rule 2) and Round D (given condition). Thus, team Y's two matches are completed in Round B and Round D.
Team B plays in Round D (given condition) and needs one more match in Round A, B, or C.
By Rule 1, Team Green (G) must play in consecutive rounds (either A & B, or B & C, or C & D). Since Round D is (B vs Y), G does not play in Round D.

Step 3: Analyze Rule 3 and Rule 5
Rule 3 states: Red (R) plays against Blue (B) in a round that is immediately before a round in which neither R nor B plays.
Rule 5 states: The team that plays against Red (R) in the match that is not against Blue (B) must be the same team that plays in Round D.

Step 4: Check for Rule 5 Violation
The teams playing in Round D are Blue (B) and Yellow (Y).
According to Rule 5, Red's other opponent (the non-B opponent of R) must be one of the teams playing in Round D.
The teams in Round D are B and Y. But Red's non-B opponent cannot be B (since that opponent is defined as the team R plays *other* than B). Therefore, Red's non-B opponent must be Yellow (Y).
However, Yellow plays in Round B and Round D.
In Round D, Yellow plays against Blue (B vs Y).
In Round B, Yellow plays its only other match. But for Yellow to also be Red's opponent, Round B would have to be (R vs Y).
If Round B is (R vs Y), then Red plays Yellow in Round B.
Now let's check Red and Blue's other matches: Red must play Blue in some round (R vs B).
Since Blue plays in Round D (B vs Y), Blue's other match (R vs B) must be in Round A or Round C.
- If (R vs B) is in Round A, then in Round B neither R nor B can play. But we established Round B has R (R vs Y), which contradicts Rule 3 (that the round immediately after R vs B must contain neither R nor B).
- If (R vs B) is in Round C, then the round after (Round D) must contain neither R nor B. But Round D is given as (B vs Y), so B plays in Round D! This contradicts Rule 3.
Hence, it is impossible to satisfy both Rule 3 and Rule 5 when Round D is (B vs Y). Specifically, the opponent link required by Rule 5 forces a direct contradiction with the schedule constraints of Rule 3 and the participation of team B in Round D.

Therefore, having (Blue vs. Yellow) in Round D violates Rule 5 (Opponent Link).