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Rita and Sam

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Rita and Sam [#permalink] New post 25 Nov 2003, 19:53
Rita and Sam....
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 [#permalink] New post 25 Nov 2003, 20:36
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!
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 [#permalink] New post 26 Nov 2003, 08:21
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
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 [#permalink] New post 26 Nov 2003, 08:57
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
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 [#permalink] New post 26 Nov 2003, 09:03
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...
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 [#permalink] New post 26 Nov 2003, 10:56
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.
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 [#permalink] New post 26 Nov 2003, 11:00
i have to agree with you, stoolfi.

i was under the wrong assumption.. my bad :(
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 [#permalink] New post 26 Nov 2003, 11:05
18, 24, 30, etc... Any multiple of six is a sure winner if you play the game correctly...

This is a nifty question.
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 [#permalink] New post 26 Nov 2003, 11:22
Yes - nice job stoolfi!

n/m

Last edited by Titleist on 26 Nov 2003, 12:27, edited 2 times in total.
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Rita and Sam [#permalink] New post 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
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 [#permalink] New post 26 Nov 2003, 11:30
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. :wink:
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 [#permalink] New post 26 Nov 2003, 11:51
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.
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 [#permalink] New post 26 Nov 2003, 12:04
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 :shock:

I hope this vague question dosent show up in my exam.

MartinMag, what is the source of this question.
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 [#permalink] New post 26 Nov 2003, 12:08
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.
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 [#permalink] New post 26 Nov 2003, 12:12
nevermind - figured it out.

Last edited by Titleist on 26 Nov 2003, 12:18, edited 1 time in total.
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 [#permalink] New post 26 Nov 2003, 12:15
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.
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 [#permalink] New post 26 Nov 2003, 12:18
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 :wink:
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 [#permalink] New post 26 Nov 2003, 12:34
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
  [#permalink] 26 Nov 2003, 12:34
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