Puzzle-19 (NASSCOM- Sample Problems)

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

Solution follows here:

Solution:

We will see both the cases here:

Roger serving first:

Number of serves for Roger = 5;     Number of serves for Rafa = 4;

Observe the following table where all possible stats are discussed:

“Five games were won by the player who did not serve” => to make this possible, columns 1 and 4 are filled first and other columns are filled accordingly.

Roger’s 5 serves		Rafa’s 4 serves
Rafa	Roger	Rafa	Roger	Rafa-Roger
1	4	0	4	8-1	not possible
2	3	1	3	3-6	not possible
3	2	2	2	5-4	not possible
4	1	3	1	7-2	not possible

Rafa serving first:

Number of serves for Rafa = 5;       Number of serves for Roger = 4;

Observe the following table where all possible stats are discussed:

“Five games were won by the player who did not serve” => to make this possible, columns 2 and 3 are filled first and other columns are filled accordingly.

Rafa's 5 serves		Roger's 4 serves
Rafa	Roger	Rafa	Roger	Rafa-Roger
4	1	4	0	8-1	not possible
3	2	3	1	6-3	only possible
2	3	2	2	4-5	not possible
1	4	1	3	2-7	not possible

The only possibility here is Rafa to serve first. Then he has 5 serves and Roger has 4 serves. Out of Rafa’s 5 serves, Roger won in 2 games (remaining 3 games won by Rafa) and Out of Roger’s 4 serves, Rafa won in 3 games (remaining 1 game won by Roger).

Answer (1)