**I n a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules: **

**(Rule 1)**** : If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. **

**(Rule 2)**** : If the number of players, say n, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n −1) players are grouped into (n −1)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament. **

**Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n + 1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament. **

**Mark (1) if Q can be answered from A alone but not from B alone.**

Mark (2) if Q can be answered from B alone but not from A alone.

**Mark (3) if Q can be answered from A alone as well as from B alone.**

**Mark (4) if Q can be answered from A and B together but not from any of them alone.**

**Mark (5) if Q cannot be answered even from A and B together.**

**1) 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.**

**2) If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n?**

**A: Exactly one player received a bye in the entire tournament.**

**B: One player received a bye while moving on to the fourth round from third round**

**(CAT 2008)**