Question

Considering Rules 1 and 2, which of the following pairs of rounds contains the Green team’s two matches?

• A. Round A and Round D
• B. Round B and Round C
• C. Round C and Round D
• D. Round A and Round B
• A. Red vs.Green
• B. Red vs.Yellow
• C. Red vs.Blue
• D. Blue vs.Yellow
• A. Green
• B. Red
• C. Yellow
• D. The opponent cannot be determined
• A. Red vs.Green
• B. Green vs.Blue
• C. Blue vs.Yellow
• D. Red vs.Yellow
• A. Round A and Round C
• B. Round A and Round D
• C. Round B and Round C
• D. Round C and Round D
• U. Freedom is a notoriously complex and contested philosophical notion, and I won’t pretend to settle any of the big controversies it raises.
• A. Red
• B. Blue
• C. Green
• D. The Yellow team plays against all other teams
• A. Rule 1 (Consecutive Play)
• B. Rule 3 (Positional Constraint)
• C. Rule 4 (Timing)
• D. Rule 5 (Opponent Link)

Answer 1

The Correct Option is B

From the complete set of constraints, the unique valid schedule that satisfies all five rules is: \[ \text{Round A: } R \text{ vs } B,\quad \text{Round B: } G \text{ vs } Y,\quad \text{Round C: } G \text{ vs } B,\quad \text{Round D: } R \text{ vs } Y. \] Here, Green (G) plays in Round B and Round C (consecutive rounds), satisfying Rule 1. Rule 2 is also satisfied since Yellow (Y) appears in Round B.

Answer 2

Rule 3 requires that Red (R) play Blue (B) in a round immediately before one in which neither R nor B appears. In the valid schedule, the only way to meet all constraints is: \[ \text{Round A: } R \text{ vs } B,\quad \text{Round B: } G \text{ vs } Y, \] so that Round B has neither R nor B. Hence, Round A must be \(\boxed{\text{Red vs.Blue}}\).

Answer 3

From the schedule: \[ \text{Round A: } R \text{ vs } B,\quad \text{Round C: } G \text{ vs } B. \] Blue (B) first appears in Round A, playing against Red (R). Hence, Red is B's first opponent.

Answer 4

Using the unique valid schedule: \[ \text{Round A: } R \text{ vs } B,\quad \text{Round B: } G \text{ vs } Y,\quad \text{Round C: } G \text{ vs } B,\quad \text{Round D: } R \text{ vs } Y. \] Thus, Round C is \(\boxed{\text{Green vs.Blue}}\).

Answer 5

Yellow (Y) plays in: \[ \text{Round B: } G \text{ vs } Y,\quad \text{Round D: } R \text{ vs } Y. \] Therefore, Y is absent from Rounds A and C, whose matches are \(R\text{ vs }B\) and \(G\text{ vs }B\) respectively.

Answer 6

From the schedule: \[ \text{Round B: } G \text{ vs } Y,\quad \text{Round D: } R \text{ vs } Y. \] So Yellow (Y) plays against Green (G) and Red (R), but never against Blue (B). Hence, the team Y does {not} play is Blue.

Answer 7

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.”} In the valid schedule, R’s matches are: \[ \text{vs } B \text{ in Round A},\quad \text{vs } Y \text{ in Round D}. \] So the non-Blue opponent of R is Yellow (Y), and that team indeed plays in Round D, satisfying Rule 5. If Round D is changed to \(B \text{ vs } Y\), then for R to still play two matches, its other opponent (not B) must be some team \(T\neq B\). Rule 5 forces this same team \(T\) to appear in Round D. But Round D is now fixed as \(B \text{ vs } Y\); thus \(T\) must be \(Y\). This makes it impossible to keep R’s original non-Blue opponent while also adjusting other matches consistently, and any attempt to re-schedule leads to a direct conflict with Rule 5. Therefore, the schedule change specifically violates Rule 5 (Opponent Link).