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
--
※ 發信站: 批踢踢實業坊(ptt.csie.ntu.edu.tw)
◆ From: 218.164.134.17