訂購 Herman Yeung 數學天書詳情

2016年5月24日 星期二

疑似 HKMO 題目 2

































































連結 Link:   IQ 題 (主頁)

連結 Link:   Herman Yeung Blog 主目錄


2 則留言:

匿名 提到...

Just to offer an alternative approach.

From equation (1),
x_2 = 1 - x_1
Also,
x_n + x_(n+1) = x_(n+1) + x_(n+2) for n=1,2,3...2014
x_n = x_(n+2) for n=1,2,3...2014

Hence,
x_1 = x_3 = x_5 = ... = x_2015 ---- (*)
and x_2 = x_4 = x_6 = ... = x_2016 = 1 - x_1 ---- (**)

From equation (2),
x_1 + x_2 + ... + x_2015 = 0 ---- (#)

Substitute (*) and (**) into #
1008 x_1 + 1007 (1 - x_1) = 0
x_1 + 1007 = 0
x_1 = -1007

Herman Yeung 提到...

thanks a lot ^^