In a game of table tennis, 24 of the 37 points played were won by the player serving, and Smith beat Jones 21-16. Remembering in table tennis that service alternates every five points, who served first?

If X is the points won by Smith on his serve and Y is the points scored by Jones on his serve.

1) X+Y =24 at all condition

Optional condition is if Smith serves first then

2) X+17-Y=21

if smiths serves second then its

3) X+20-Y=21

3) doesnt give integer solution so X-Y=4 or X=14 and Y=10

Hences jones serves last.

Here there are two options is Smiths wins a) 2-0 in last serve or b) 1-1 in last serve

In case a) the scores would be 14/6 on Smith serve and 7/10 on Jones serve and Case b) the scores would be 14/6 on smith serve and 7/10 on Jones Serve. So it really doesnt make any difference as regards score in the final serve.

So Smith Serves first.

 

Posted by Salil on 2013-07-18 08:13:54