AMC数学竞赛真题2016年B 3-4

AMC10数学竞赛是美国高中数学竞赛中的一项，是针对高中一年级及初中三年级学生的数学测试，该竞赛开始于2000年，分A赛和B赛，于每年的2月初和2月中举行，学生可任选参加一项即可。不管是对高校申请还是今后在数学领域的发展都极其有利！那么接下来跟随小编来看一下AMC10数学竞赛真题以及官方解答吧：

Problem 3

Let . What is the value of  ?

Solution

Substituting carefully,

becomes which is .

Solution 2

Solution by e_power_pi_times_i

Substitute into the equation. Now, it is . Since , it is a positive number, so . Now the equation is . This further simplifies to , so the answer is

Problem 4

Zoey read books, one at a time. The first book took her day to read, the second book took her days to read, the third book took her days to read, and so on, with each book taking her more day to read than the previous book. Zoey finished the first book on a Monday, and the second on a Wednesday. On what day the week did she finish her th book?

Solution

The process took days, so the last day was days after the first day. Since is divisible by , both must have been the same day of the week, so the answer is . 

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