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.

Team Opponent Check Which team does the Yellow team NOT play against over the course of the four rounds?

The correct option is Blue.

Let us analyze the rules step-by-step to deduce the schedule of matches for the four rounds (Round A, Round B, Round C, Round D).

Given Information:
- 4 rounds: Round A, Round B, Round C, Round D.
- 4 teams: Red (R), Blue (B), Green (G), Yellow (Y).
- Each round consists of 1 match between 2 teams (so 2 teams play in each round).
- Each team plays exactly 2 matches in total across the 4 rounds.
- No two teams play each other more than once.

Step-by-step Deduction:

1. Analyze Rule 3 (Positional Constraint):
Rule 3 states: "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."
- Since R vs B is a round where R and B play, the round immediately after it has neither R nor B playing.
- Therefore, the match R vs B cannot be in Round D (because Round D is the final round, so there is no round immediately after it).
- Thus, R vs B must be in Round A, B, or C.
- If R vs B is in Round A, then neither R nor B plays in Round B.
- If R vs B is in Round B, then neither R nor B plays in Round C.
- If R vs B is in Round C, then neither R nor B plays in Round D.

2. Analyze Rule 2 & Round B:
- Rule 2 states that Yellow (Y) must play in Round B.
- If R vs B were in Round A, neither R nor B plays in Round B, so Round B must involve Y and G (since only 2 teams play per round).
- If R vs B were in Round B, then R and B play each other in Round B. But Rule 2 requires Y to play in Round B. Since only 2 teams play per round, Round B cannot be R vs B.
- Therefore, R vs B cannot be in Round B.

3. Analyze Rule 4 (Timing):
- Rule 4 states: "The Blue team's (B) first match must occur in an earlier round than the Green team's (G) first match."
- If R vs B is in Round C, B's first match could be Round C or earlier.
- If B's first match is in Round C, G's first match must be in Round D (to be later than B's). But G must play 2 matches in consecutive rounds (Rule 1), which is impossible if G's first match is in Round D (the last round).
- If B's first match is earlier than Round C (i.e., Round A or B), then let's test if R vs B can be in Round A.

4. Testing R vs B in Round A:
- Round A: R vs B.
- B's first match is in Round A.
- By Rule 3, neither R nor B plays in Round B.
- By Rule 2, Y plays in Round B. Since neither R nor B plays in Round B, the match in Round B must be G vs Y.
- G's first match is in Round B (which satisfies Rule 4, since Round A < Round B).
- By Rule 1, Green (G) must play consecutive matches. Since G's first match is Round B, G's second match must be in Round C.
- In Round C, G must play against R or B (since Y already played G, and no repeat matches allowed).
- Let's check Rule 5: "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."
- R plays against B in Round A. R's second match must be against G or Y.
- If R plays G in Round C (so Round C is R vs G), then R's opponent (not B) is G. According to Rule 5, G must be one of the teams playing in Round D.
- Then Round D would be B vs Y (since R played in Round A & C, G played in Round B & C, so Round D must be between B and Y). Here, G is not playing in Round D, which contradicts Rule 5.
- If Round C is G vs B, then B plays G in Round C. Then R's second match must be in Round D against Y (so Round D is R vs Y).
- Here, R's opponent in the non-B round is Y. And Y plays in Round D! This satisfies Rule 5 perfectly!

5. Verify the complete schedule:
- Round A: Red (R) vs Blue (B)
- Round B: Green (G) vs Yellow (Y)
- Round C: Green (G) vs Blue (B)
- Round D: Red (R) vs Yellow (Y)

Let's double check all rules against this schedule:
- Each team plays 2 matches: R (Rounds A, D), B (Rounds A, C), G (Rounds B, C), Y (Rounds B, D). (Satisfied)
- Rule 1: G plays in Rounds B and C (consecutive). (Satisfied)
- Rule 2: Y plays in Round B. (Satisfied)
- Rule 3: R vs B is in Round A. Immediately after (Round B), neither R nor B plays. (Satisfied)
- Rule 4: B's first match is Round A, G's first match is Round B (A < B). (Satisfied)
- Rule 5: R's match not against B is in Round D against Y. The team Y is indeed playing in Round D. (Satisfied)

6. Determine Yellow's opponents:
- Yellow plays against Green (G) in Round B.
- Yellow plays against Red (R) in Round D.
- Therefore, Yellow plays against Green and Red, but does NOT play against Blue.