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# Rita and Sam

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Senior Manager
Joined: 22 May 2003
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Location: Uruguay
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Rita and Sam [#permalink]  25 Nov 2003, 19:53
Rita and Sam....
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Director
Joined: 14 Oct 2003
Posts: 588
Location: On Vacation at My Crawford, Texas Ranch
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Kudos [?]: 10 [0], given: 0

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: 334
Location: Uruguay
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Kudos [?]: 41 [0], given: 0

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: 971
Location: Florida
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Kudos [?]: 35 [0], given: 0

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,R---last with be Sam's. whatever rita choose
Senior Manager
Joined: 22 May 2003
Posts: 334
Location: Uruguay
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Kudos [?]: 41 [0], given: 0

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: 503
Location: 55405
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Kudos [?]: 11 [0], given: 0

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.

Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
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Kudos [?]: 35 [0], given: 0

i have to agree with you, stoolfi.

i was under the wrong assumption.. my bad
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
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Kudos [?]: 11 [0], given: 0

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: 588
Location: On Vacation at My Crawford, Texas Ranch
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Kudos [?]: 10 [0], given: 0

Yes - nice job stoolfi!

n/m

Last edited by Titleist on 26 Nov 2003, 12:27, edited 2 times in total.
Intern
Joined: 24 Nov 2003
Posts: 30
Location: Champaign
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Kudos [?]: 3 [0], given: 0

Rita and Sam [#permalink]  26 Nov 2003, 11:22
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: 971
Location: Florida
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Kudos [?]: 35 [0], given: 0

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
Followers: 0

Kudos [?]: 3 [0], given: 0

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
Followers: 0

Kudos [?]: 3 [0], given: 0

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: 971
Location: Florida
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Kudos [?]: 35 [0], given: 0

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: 588
Location: On Vacation at My Crawford, Texas Ranch
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Kudos [?]: 10 [0], given: 0

nevermind - figured it out.

Last edited by Titleist on 26 Nov 2003, 12:18, edited 1 time in total.
Intern
Joined: 24 Nov 2003
Posts: 30
Location: Champaign
Followers: 0

Kudos [?]: 3 [0], given: 0

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: 971
Location: Florida
Followers: 1

Kudos [?]: 35 [0], given: 0

rita takes 1st 1-5, sam takes 5-1, rita 1-5, sam wins.
sam will play only after considering rita's moves. He ia a PRO
Senior Manager
Joined: 22 May 2003
Posts: 334
Location: Uruguay
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Kudos [?]: 41 [0], given: 0

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
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