作者chaogold (dchaodx)
看板IMO_Taiwan
標題Re: 從雲飄飄轉來的...放在這比較多人看~
時間Fri Sep 12 23:38:22 2003
※ 引述《myflame (龍隊 紅隊 太陽隊)》之銘言：
: 感謝chaogold提供題目
: 1. In triangle ABC prove that a + b + c < r_1 + r_2 + r_3 + min {r_1,r_2,r_3}
: where r_1 is the exradius opposite a, r_2 is the exradius opposite b and r_3
: is the exradius opposite c.
: 2. How can you arrange numbers from 1 to 2003 in a row so that avg. of any
: two numbers doesn't lie between them? E.g. 2003...1002...1 is invalid as
: (1+2003)/2=1002
: 3.Prove that there are infinitely many primes that can be written as the sum
: of a prime and a power of two.
: 4. [x/(y+z)]^(1/2) + [y/(x+z)]^(1/2) + [z/(y+x)]^(1/2) > 2
第二題學長的解法太妙了！
我只能說妙..
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