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# Rita and Sam play the following game with n sticks on a

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CEO
Joined: 15 Aug 2003
Posts: 3454
Rita and Sam play the following game with n sticks on a [#permalink]

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09 Oct 2003, 20:38
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1. Rita and Sam play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is the value of n such that Sam can always win no matter how Rita plays?

A. 7

B. 10

C. 11

D. 12

E. 16
SVP
Joined: 03 Feb 2003
Posts: 1604

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14 Oct 2003, 01:31
Rita can win if N is odd and either person takes one stick at a time. So, 7 and 11 are out. Consider 10, 12, and 16. Sam should always win.

10=5(Rita)+5(Sam)+1(Rita) Rita can win
12=5(Rita)+5(Sam)+2(Rita) Rita can win

So, 16 is left.
SVP
Joined: 30 Oct 2003
Posts: 1790
Location: NewJersey USA

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31 Dec 2003, 12:16
The answer is 12

If Sam wants to win then there should be 6 sticks left at the end and it is Rita's turn to pick. This means Sam would have picked 1-5 sticks. So Sam should have atleast one stick left prior to this trial. If atleast one stick is left then it should be so even if Rita picks up max number of sticks

so 5+1+6 = 12
Director
Joined: 28 Oct 2003
Posts: 501
Location: 55405

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31 Dec 2003, 20:03
31 Dec 2003, 20:03
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# Rita and Sam play the following game with n sticks on a

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