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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Rita and Sam play the following game with n sticks on a table. Each mu
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20 Sep 2021, 04:47
20 Sep 2021, 04:47
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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 a value of n such that Sam can always win no matter how Rita plays?
A. 7
B. 10
C. 11
D. 12
E. 16
A. 7
B. 10
C. 11
D. 12
E. 16
Re: Rita and Sam play the following game with n sticks on a table. Each mu
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23 Sep 2021, 01:47
23 Sep 2021, 01:47
Expert Reply
If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).
Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.
The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.
Answer: D.
Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.
The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.
Answer: D.
gmatclubot
Re: Rita and Sam play the following game with n sticks on a table. Each mu [#permalink]
23 Sep 2021, 01:47
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