# Homework Help: Logic problem about tennis

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1. Jul 29, 2017

### Terrell

1. The problem statement, all variables and given/known data
Pat beat Stacy in a set of tennis, winning six games to Stacy’s three. Five games were won by the player who did not serve. Who served first?
source: https://ocw.mit.edu/courses/mathematics/18-s34-problem-solving-seminar-fall-2007/assignments/hw8.pdf
2. Relevant equations
N/A

3. The attempt at a solution
Since Pat won 6 games which is at least 5 games then she is the player who did not serve. Since Pat never served then she could not be the one who served first. Therefore, Stacy. Is my line of reasoning correct?

2. Jul 29, 2017

### SammyS

Staff Emeritus
No. Your line of reasoning has at least one error and could use a bit more explanation.

In tennis, the serve alternates in a given set, from one game to the next.

There were 9 games, so one of the players served 5 games, the other 4.

Therefore, it's wrong to say that "Pat never served".

3. Jul 31, 2017

### haruspex

This could have been clearer: five games were won by the player who was not the server in that game.

4. Aug 1, 2017

### Kaura

Since the server alternates and either one could have been the first server the only possible set of servers can be PSPSPSPSP or SPSPSPSPS

5. Aug 1, 2017

### scottdave

One thing that you can deduce is that Pat won the last game (ending the set). It is sort of obvious, but should help in determining who served on that game.

6. Aug 1, 2017

### scottdave

I was able to work out a scenario for one of the players starting the serve, but not yet with the other one. I am guessing that this is what they were looking for.

7. Aug 1, 2017

### haruspex

@Terrell, it looks like you are unfamiliar with the rules of tennis. You need to know that the set ends if one player has won six games and the other fewer than 5.
So who won the last game?

8. Aug 1, 2017

### Terrell

let me clarify. Do I need to win a set first so I can win each remaining set with only 5 games? I'm totally unfamiliar to the rules except I need to be the first one to win 6 games within a set to win that set.

9. Aug 1, 2017

### SammyS

Staff Emeritus
Did you read each of the replies ?

10. Aug 1, 2017

### Terrell

But the problem directly stated "Five games were won by the player who did not serve". What does the problem mean by that?

11. Aug 1, 2017

### Terrell

If my understanding of the problem is correct. The player who won is the player winning each of the 5 games she did not serve? So it must be the scenario: SPSPSPSPS. Therefore, Stacy served first is the answer.

12. Aug 1, 2017

### Terrell

that is a hundred times clearer for me. thanks!

13. Aug 1, 2017

### SammyS

Staff Emeritus
Yes, and Pat won each of the 5 games in which Stacy served, plus one more - one of the games in which Pat served.

Ignore this post of mine. Obviously it is incorrect.

Last edited: Aug 2, 2017
14. Aug 1, 2017

### Terrell

thank you!

15. Aug 1, 2017

### haruspex

No. In each game, one player serves, the other receives. Five of the games were won by the receiver in that game. Some of these may have been won by Pat, the rest by Stacy.

16. Aug 1, 2017

### haruspex

17. Aug 1, 2017

### haruspex

That makes no sense.
There is only one set here. It consists of a sequence of games.
Yes. (There is a bit more to it, but not that's relevant to this question.)
And of course the set ends as soon as someone has won it. So who won the last game?

18. Aug 2, 2017

### rcgldr

Even if you don't know the rules of tennis, the problem states that Pat won 6 games, Stacy won 3 games. There were no other games played. As posted previously, the set ended when Pat won for the 6th time.

19. Aug 2, 2017

### Terrell

okay. that complicates things. hmmm

20. Aug 2, 2017

### scottdave

Not necessarily. There were a total of 9 games played. Each of those games was won by a person. They tell you that 5 of those 9 games were won by the person who received (did not serve for that game). So you know that 4 of the games were won by a person that served.

It may be that Pat won 5 games that she received in, or maybe some other combination that can be figured out. It should be obvious that Pat achieved the 6th win on the last game, ending the set.

We have two serve possibilities: PSPSPSPSP or SPSPSPSPS. Take one of these, and look at Pat winning the last game. Then see if you can fit the other criteria. Then look at the other possibility, see if you can fit the criteria into that one.

21. Aug 2, 2017

### haruspex

You need to create some variables so that you can write some equations.
Let the number of games where Pat served and won be one of them, and similarly three more.
What equations can you then write?

22. Aug 5, 2017

### rcgldr

It's been a few days, should we offer more hints?

23. Aug 5, 2017

### haruspex

I vote not. I gave @Terrell plenty to work with in post #21. Looks like he/she has just lost interest.

24. Aug 5, 2017

### SammyS

Staff Emeritus
I agree.

25. Aug 5, 2017

### rcgldr

I was thinking of other people that might be curious about the solution, although anyone that know tennis well shouldn't have an issue with this problem.