2003年AMC10竞赛B第22题
一个钟在半点时响一次，在整点时，几点钟就响几次．例如，在下午$$1$$点有一次报时，在正午$$12$$点和午夜$$12$$点各有$$12$$次报时．从$$2003$$年$$2$$月$$26$$日上午$$11$$点$$15$$分开始，第$$2003$$次报时将在哪一天发生？
课内体系->知识点->等式与不等式->等式->方程组的解集 美国AMC10/12->Knowledge Point->Combination->Reasoning->Recurrence and Recursion
First, find how many chimes will have already happened before midnight (the beginning of the day) of February $$27$$, $$2003$$. $$13$$ half-hours have passed, and the number of chimes according to the hour is $$1+2+3+\cdots +12$$. The total number of chimes is $$13+78=91$$.  Every day, there will be $$24$$ half-hours and $$2(1+2+3+\cdots 12)$$ chimes according to the arrow, resulting in $$24+156=180$$ total chimes.  On February $$26$$, the number of chimes that still need to occur is $$2003-91=1912$$. $$1912\div 180=10\rm R112$$. Rounding up, it is $$11$$ days past February $$26$$, which is March $$9$$. 