首页
登录
职称英语
Rita and Sam play the following game with n sticks on a table. Each must remove
Rita and Sam play the following game with n sticks on a table. Each must remove
游客
2024-01-13
41
管理
问题
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?
选项
A、7
B、10
C、11
D、12
E、16
答案
D
解析
Let Player A be either Rita or Sam, and let Player B be the other player. If, after one of Player A’s turns, there are exactly 6 sticks left, then Player A can win on his or her next turn This is because if 6 sticks are left after Player A’s turn, then regardless of whether Player B removes 1,2, 3, 4, or 5 sticks, it follows that Player A can win on his or her next turn by removing, respectively, 5,4,3,2, or 1 stick.
n = 7
: If Rita begins by removing 1 stick, then there will be 6 sticks left after Rita’s turn. Therefore, by the remarks above, Rita can win Hence, Sam cannot always win.
n = 10
: If Rita begins by removing 4 sticks, then there will be 6 sticks left after Rita’s turn Therefore, by the remarks above, Rita can win. Hence, Sam cannot always win.
n = 11
: If Rita begins by removing 5 sticks, then there will be 6 sticks left after Rita’s turn Therefore, by the remarks above, Rita can win. Hence, Sam cannot always win.
n = 12
: If Rita begins by removing 1 stick, the n Sam can win by removing 5 sticks on his next turn, because 6 sticks will remain after Sam’s turn. If Rita begins by removing 2 sticks, then Sam can win by removing 4 sticks on his next turn, because 6 sticks will remain after Sam’s turn. By continuing in this manner, we see that if Rita begins by removing k sticks (where k is one of the numbers 1,2,3,4, or 5), then Sam can vin by removing (6-k) sticks on his next turn because 6 sticks will remain after Sam’s turn. Therefore, no matter how many sticks Rita removes on her first turn, Sam can win by removing appropriate numbers of sticks on his next two turns. Hence, Sam can always win.
n = 16
: If Rita removes 4 sticks on her first turn, then Sam will be in the same situation as Rita for n = 12 above, and therefore Rita can win no matter what Sam does. Hence, Sam cannot always win.
The correct answer is D.
转载请注明原文地址:https://tihaiku.com/zcyy/3360150.html
相关试题推荐
Allthefollowingcasesareon-the-jobsmokingexceptthat______.[br]Passives
Inmakingmarketinvestigation,oneshould______.[br]Whichofthefollowings
In1863,AbrahamLincolnwas______.[br]WhichofthefollowingstatementsisN
TheWord"here"(Para,1,Line3)refersto______.[br]Whichofthefollowing
Whichofthefollowingcanbeinferredfromthepassage?[br]Thebestconclusio
Whichofthefollowingcanbeinferredfromthepassage?[br]Accordingtothea
WhiletakingataxiinFinland,______.[br]WhichofthefollowingisNOTtrue
Thepassageismainlyabout______.[br]WhichofthefollowingdoesRebeccaDres
Thefirstuseofumbrellawasas______.[br]Whichofthefollowingmaybethe
WhichofthefollowingisNOTtrueaccordingtothepassage?[br]Theword"affe
随机试题
Before,wheneverwehadwealth,westarteddiscussingpoverty.Whynotnow?
Michelangelo’sMasterpiece:DavidIn1501,25-yea
[originaltext]W:Excuseme,doyouknowifthistableistaken?M:Idon’tthi
ThebiggestproblemfacingChileasitpromotesitselfasatouristdestina
胰腺癌术后胆瘘并发症发生的时间一般在( )。A.5~10天 B.3~4天 C
下列说法中,正确的有() (1)2004~2008年我国国内生产总值呈逐
下列对艾滋病病毒(HIV)复制过程,不正确的描述是A.GP120与T4淋巴细胞
治疗内伤咳嗽的主穴为A.太渊 B.三阴交 C.肺俞 D.脾俞
气滞便秘的辨证特点是( ) A.面赤身热,口臭唇焦,尿赤,苔黄燥,脉滑实
关于最低评标价法的说法,正确的有()。A.该方法适用于具有通用技术,性能标
最新回复
(
0
)