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.

Identifying the Blue Team’s First Opponent Who is the Blue team’s first opponent in the tournament?

The correct option is Red.

Let's analyze the given rules step-by-step to deduce the complete schedule of the tournament consisting of 4 rounds: Round A, Round B, Round C, and Round D.

1. Understanding the Tournament Rules:

• There are 4 teams: Red (R), Blue (B), Green (G), and Yellow (Y).
• There are 4 rounds: A, B, C, and D, with 1 match per round (2 teams per match).
• Total team slots across 4 rounds = 4 × 2 = 8 slots.
• Every team plays exactly 2 matches, meaning each team appears exactly twice in the schedule.
• No team plays the same opponent twice.

2. Deductive Analysis of Team Schedules:

• Rule 3: Red (R) plays against Blue (B) in a round immediately before a round in which neither R nor B plays.
This means the match (R vs B) cannot be in Round D, because Round D is not immediately followed by any round. Thus, (R vs B) must occur in Round A, Round B, or Round C.
Furthermore, the round immediately after (R vs B) must consist of the remaining two teams: Green (G) and Yellow (Y).

• Rule 1 & Rule 4:
Rule 1 states Green (G) plays in two consecutive rounds.
Rule 4 states Blue's (B) first match occurs before Green's (G) first match.
Since B's first match is earlier than G's first match, G cannot play in Round A. Therefore, G's consecutive matches must be either in Rounds B and C, or in Rounds C and D.

• Let's test the possibility of G playing in Rounds B and C:
If G plays in B and C, then since G plays consecutive rounds, G's first match is in Round B. By Rule 4, B's first match must be in Round A.
If B plays in Round A, and Round A is followed by Round B (which contains G), neither R nor B can be playing in Round B if Round A was (R vs B).
So, if Round A is (R vs B), then Round B must be (G vs Y) (since Y plays in Round B by Rule 2, and neither R nor B plays in Round B).
Then G's second match is in Round C.
This setup satisfies all conditions seamlessly!

3. Verifying the Round A Match:

In Round A, the match played is between Red (R) and Blue (B).
Since this is Round A (the very first round of the tournament), this match is the first match for both the Red team and the Blue team.

Therefore, the Blue team's first opponent in the tournament is the Red team.