Comprehension

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.

(193 words)

Question: 1

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

Show Hint

Once you find a schedule that satisfies {all} constraints, read off direct facts (like who plays when) instead of re-solving for each question.
Updated On: Jul 3, 2026
  • Round A and Round D
  • Round B and Round C
  • Round C and Round D
  • Round A and Round B
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: List the fixed pairings for each round: Round A = Red vs Blue, Round B = Green vs Yellow, Round C = Green vs Blue, Round D = Red vs Yellow.
Step 2: Pick out the rounds where Green appears.
\[ \boxed{\text{Round B and Round C}} \]
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Question: 2

Based on all the rules, particularly Rule 3, which of the following matches must be scheduled for Round A?

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For “immediately before” constraints, try placing the special match in each possible round and see which positioning lets the next round omit the required teams.
Updated On: Jul 3, 2026
  • Red vs.Green
  • Red vs.Yellow
  • Red vs.Blue
  • Blue vs.Yellow
Show Solution

The Correct Option is C

Solution and Explanation

Rule 3 ties Red and Blue to a round that must be followed by one where neither of them appears. The only way to satisfy this across four rounds is for Red to face Blue in Round A, immediately before Green plays Yellow in Round B, a round with no Red or Blue at all. So Round A has to be Red vs Blue.
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Question: 3

Who is the Blue team's (B) first opponent in the tournament?

Show Hint

When a rule mentions “first match,” always check the earliest round in which that team appears in the final schedule.
Updated On: Jul 3, 2026
  • Green
  • Red
  • Yellow
  • The opponent cannot be determined
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Find every round Blue plays in: Round A and Round C.
Step 2: Take the earlier one, Round A, which pairs Red against Blue.
\[ \boxed{\text{Red}} \]
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Question: 4

What is the match scheduled for Round C?

Show Hint

After constructing the schedule, many later questions become simple look-ups rather than fresh logic problems.
Updated On: Jul 3, 2026
  • Red vs.Green
  • Green vs.Blue
  • Blue vs.Yellow
  • Red vs.Yellow
Show Solution

The Correct Option is B

Solution and Explanation

Round A and Round D are already taken up by Red vs Blue and Red vs Yellow. That leaves Green and Blue as the only teams not yet paired for Round C, so the match scheduled for Round C is Green vs Blue.
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Question: 5

Which pair of rounds contains matches where the Yellow team (Y) does {not participate?}

Show Hint

List each team’s rounds explicitly; then it is easy to see in which rounds they are missing.
Updated On: Jul 3, 2026
  • Round A and Round C
  • Round A and Round D
  • Round B and Round C
  • Round C and Round D
  • Freedom is a notoriously complex and contested philosophical notion, and I won’t pretend to settle any of the big controversies it raises.
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Identify Yellow's two rounds: Round B and Round D.
Step 2: The two rounds left over, where Yellow does not appear, are Round A and Round C.
\[ \boxed{\text{Round A and Round C}} \]
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Question: 6

Which team does the Yellow team (Y) {not play against over the course of the four rounds?}

Show Hint

To answer “does not play” questions, write down all opponents of the team and compare with the full list of teams.
Updated On: Jul 3, 2026
  • Red
  • Blue
  • Green
  • The Yellow team plays against all other teams
Show Solution

The Correct Option is B

Solution and Explanation

Since every team gets exactly two matches, and Yellow's two are already used up by Green (Round B) and Red (Round D), there is no match left over for Yellow to meet Blue. So Blue is the team Yellow never plays against.
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Question: 7

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

Show Hint

When testing a hypothetical change, ask: “Is there {any} way to build a schedule with this change that still satisfies each rule?” The first rule that makes this impossible is the one being violated.
Updated On: Jul 3, 2026
  • Rule 1 (Consecutive Play)
  • Rule 3 (Positional Constraint)
  • Rule 4 (Timing)
  • Rule 5 (Opponent Link)
Show Solution

The Correct Option is D

Solution and Explanation

Rule 5 links Red's non-Blue opponent specifically to Round D. That non-Blue opponent is Yellow, so the rule needs Yellow to be the team appearing in Round D alongside someone else consistent with the link. If Round D is instead fixed as Blue vs Yellow, Red is squeezed out of any round that satisfies this link, so the rule that breaks is Rule 5 (Opponent Link).
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