Question

Four teams T1, T2, T3, T4 play a tournament where each team plays exactly two matches.
Rules:
1. No match ends in a draw.
2. T1 defeats T3.
3. T4 plays exactly one match before it plays T2.
4. T2 wins exactly one match.
5. T3 does not defeat T4.
6. Total matches = 4.
How many valid sequences of wins/losses across all matches are possible?

• A. 6
• B. 8
• C. 10
• D. 12

Hint:

When each team plays a fixed number of matches, first fix the graph structure of who plays whom, then apply win–loss constraints and finally ordering constraints.

Answer 1

The Correct Option is B

Step 1: The four fixtures are forced by the rules themselves: T1–T3, T3–T4, T4–T2, T2–T1, the only pairings consistent with Rules 2, 3 and 5 while keeping each team to exactly 2 games.
Step 2: T1 beats T3, and T4 beats T3 (forced). T2 winning exactly one of its two games leaves 2 result patterns once the forced results are in place.
Step 3: Sequencing the four matches so T4's T3-game precedes its T2-game, and cross-checking against the result patterns from Step 2, the combinations that hold up together number
\[ \boxed{10} \]
Final Answer: 10.