Vemuri's Brain Teaser-5

[mathbyvemuri]

In tennis, service alternates for each game between the two players and the first player to win 6 games wins. A player winning 6-2 indicates that 8 games were played, of which the winning player won 6 and loosing player won 2.
Rafa beat roger in a set of tennis, winning 6 games to Roger's three. Five games were won by the player who did not serve. Who served first?
(1)Rafa (2) Roger (3) Inconsistent (4) Indeterminate

[eagleeye]

It is Rafa serving first. .

Let Rafa be A, and Roger be O (I am choosing the second letters for each player's name).

Then we have 6 wins for A, and 3 wins for O. Since the games went till 9 games, the last game must have been won by A. Also, we are given that 5 wins came for the players while they weren't serving. Then, by standard Tennis rules, the serves must alternate. So we can have only two possibilities (other than the data being inconsistent) for the order of the serves:

Either A/O/A/O/A/O/A/O/A
Or O/A/O/A/O/A/O/A/O

Now we know that the last game must have been won by A (Otherwise the match would have ended at game 8, so we really don't care about the last one). Now for the rest, let's consider matching the winner/loser data with the options. I am going to represent A winning by a, and O winning by o.

Then: For the first possibility of Serves, we have one possibility that:
Game: 1/2/3/4/5/6/7/8/9
Wins: a/a/o/a/o/a/a/o/a
Serves: A/O/A/O/A/O/A/O/A

In this case, data is consistent since we have 3 wins for O, 5 wins when the players are not serving (Note the wins vs serves rows and compare columns for 2/3/4/5/6) and total 6 wins for A.

Now let's consider the other possibility of Serves:
Game: 1/2/3/4/5/6/7/8/9
Wins: o/a/a/a/o/o/a/a/a
Serves: O/A/O/A/O/A/O/A/O

In this case, data will not fit because the last column of wins vs serves has opposite elements. Since we can have only 5 games where players serving did not win, this means that of the other 8 games, 4 columns have to have opposite letters in wins vs games. So, we would have 2 o, 2a. But having it this way would mean that for the other 4 games, because the players serving must win, we have 2 more o, and 2 more a. This is inconsistent with our original condition of 6a, 3o. Hence this cannot be the case. Consequently, the correct answer is 1.

Let me know if this helps and if I got it right

[mathbyvemuri]

It is Rafa serving first. .

Let me know if this helps and if I got it right

hats off,you are right.