Question

What is the number of matches played by the champion?
A. The entry list for the tournament consists of 83 players.
B. The champion received one bye.

• A. If A alone but not B alone is sufficient
• B. If B alone but not A alone is sufficient
• C. If both A and B together are sufficient
• D. If A alone is sufficient and B alone is sufficient
• E. If not even A and B together are sufficient

Hint:

In elimination tournaments, champion’s matches depend only on total players, not on the structure of byes.

Answer 1

The Correct Option is A

From A: In a single elimination with 83 players, the champion must win enough matches to remain last. Each match eliminates 1 player, so to be champion you must be the only undefeated after \(83 - 1 = 82\) eliminations. The champion’s matches = total rounds played (logically \(\lceil \log_2 83 \rceil\) with some byes). The exact count can be deduced from A alone. From B: Knowing only that the champion got one bye does not give the exact count of matches — total participants unknown. Thus, A alone is sufficient, B alone is not.