2010年AMC10竞赛A第10题
马文在闰年$$2008$$年的$$5$$月$$27$$日星期二过生日．他下一个星期六的生日是在哪一年？
美国AMC10/12->Knowledge Point->Combination->Reasoning->Recurrence and Recursion 课内体系->知识点->推理与证明->逻辑推理题
$$\boxed{\rm(E)}2017$$.  There are $$365$$ days in a non-leap year. There are $$7$$ days in a week. Since $$365=52\cdot7+1$$(or $$365$$ is congruent to $$1\textasciitilde\rm mod\textasciitilde7$$), the same date (after February) moves "forward" one day in the subsequent year, if that year is not a leap year.  For example:  $$5/27/08$$ Tue  $$5/27/09$$ Wed  However, a leap year has $$366$$ days, and $$366=52\cdot7+2$$. So the same date (after February) moves "forward" two days in the subsequent year, if that year is a leap year.  For example: $$5/27/11$$ Fri  $$5/27/12$$ Sun  You can keep count forward to find that the first time this date falls on a Saturday is in $$2017$$:  $$5/27/13$$ Mon  $$5/27/14$$ Tue  $$5/27/15$$ Wed  $$5/27/16$$ Fri  $$5/27/17$$ Sat 