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Direction for the below question:

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

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

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

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

Mark $(5)$ if Q cannot be answered even form A and B together.

In a single elimination tournament, any players is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:

  1. If the number of players, say $n$ in any round is even, then the players get 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.
  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 in to $(n-1)/2$ 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 played between two players. The winner in the final round is the champion of the tournament.

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

  1. Exactly one player received a bye in the entire tournament.
  2. One player received a bye while moving on to the fourth round from the third round
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