Author 
Message 
Senior Manager
Joined: 22 May 2003
Posts: 329
Location: Uruguay

Rita and Sam [#permalink]
Show Tags
25 Nov 2003, 20:53
This topic is locked. If you want to discuss this question please repost it in the respective forum. Rita and Sam....
Attachments
Rita and Sam.jpg [ 16.12 KiB  Viewed 1137 times ]



Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch

16  Relatively simple question  just matter of reading the question first and then testing the answer choices.
Also divide 1,2,3,4,5 into 16. Sam will always have last picks on an even number. 3 and 5 leave a remainder  leaving Sam with last pick!
Cheers!



Senior Manager
Joined: 22 May 2003
Posts: 329
Location: Uruguay

I am not getting this... Could you give a more thorough explanation please?
If n=16 for example Rita could draw 1, then Sam could draw 5, then Rita could draw 4 leaving 6 sticks, and no matter what Sam draws next she would have last picks.
Like I said... I'm not getting this



Director
Joined: 13 Nov 2003
Posts: 960
Location: Florida

you made me think over this..
total sticks are 16 and you can choose only 5 possible numbers.
lets sum these 1+2+3+4+5 = 15. so the last draw will always be of Sam.
or,
R,S,R,S,Rlast with be Sam's. whatever rita choose



Senior Manager
Joined: 22 May 2003
Posts: 329
Location: Uruguay

I don't see the point in adding 1+2+3+4+5 since each player can decide the number of sticks to retrieve from the pack in each draw. For example Sam could draw 1 stick every time... or 5 sticks every time he draws...



Director
Joined: 28 Oct 2003
Posts: 501
Location: 55405

If Rita goes 1st, and there are 12 sticks:
She takes one, sam takes 5, leaves her with 6
she takes 2, sam takes 4, sam leaves her with 6
she takes 3, sam takes 3, sam leaves her with 6
she takes 4, sam takes 2, sam leaves her with 6
she takes 5, sam takes 1, sam leaves her with 6.
if she is left with six, she will leave sam with five or fewer. Sam will win.
12 is the answer.



Director
Joined: 13 Nov 2003
Posts: 960
Location: Florida

i have to agree with you, stoolfi.
i was under the wrong assumption.. my bad



Director
Joined: 28 Oct 2003
Posts: 501
Location: 55405

18, 24, 30, etc... Any multiple of six is a sure winner if you play the game correctly...
This is a nifty question.



Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch

Yes  nice job stoolfi!
n/m
Last edited by Titleist on 26 Nov 2003, 13:27, edited 2 times in total.



Intern
Joined: 24 Nov 2003
Posts: 30
Location: Champaign

Rita and Sam [#permalink]
Show Tags
26 Nov 2003, 12:22
12 cannot be the asnwer:
Rita takes 5, then Sam takes 5, Rita is left with 2  Rita wins.
My assumption is that  lets not try to make them win but see no matter what Sams or Rita does Sams wins.
Since for alll the numbers Rita can win, I go with 16
Correct me if I am wrong



Director
Joined: 13 Nov 2003
Posts: 960
Location: Florida

the basic assumption you should take in the ques is "sam win whatever rita plays"...sam will make his moves depending on what rita does...he will not play a random game...
until and unless it is specified that "sam's play doesn't depend on rita's play" if I consider this case .... hmmm....I didn't get an answer.



Intern
Joined: 24 Nov 2003
Posts: 30
Location: Champaign

Welll u have a point reg. my assumption  yes then we are lost.
So what is the conclusion 12 or 16  I am totally confused now after reading the question again.



Intern
Joined: 24 Nov 2003
Posts: 30
Location: Champaign

Well then how can we explain:
R 5
S 1
R 5
S 1
So 12 can be the asnwer. Now I am further lost
I hope this vague question dosent show up in my exam.
MartinMag, what is the source of this question.



Director
Joined: 13 Nov 2003
Posts: 960
Location: Florida

Sam to win: we should be left with 6 or a multiple of 6. 12 is the answer
maverick, just consider this simple trick in these kinda ques.



Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch

nevermind  figured it out.
Last edited by Titleist on 26 Nov 2003, 13:18, edited 1 time in total.



Intern
Joined: 24 Nov 2003
Posts: 30
Location: Champaign

I agree with u explaination  because that is how I visualized it and I will stop bugging ppl more with my posts  because I am gonna confuse myself even further.
Thanks again to u guys for explaining.



Director
Joined: 13 Nov 2003
Posts: 960
Location: Florida

rita takes 1st 15, sam takes 51, rita 15, sam wins.
sam will play only after considering rita's moves. He ia a PRO



Senior Manager
Joined: 22 May 2003
Posts: 329
Location: Uruguay

The question is from VStudy and the answer given is 12.
Now I finally see it, thanks guys. Was pretty simple after all. It does get tricky if you think too much doesn't it? (I hate it when that happens)
Martin










