## Thursday, 3 November 2011

### 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).