IIT JEE , AIEEE Forum - Mathematics , Algebra - a1,a2,...a2007 are 1,2,.....2007 in same order. if 'x' is the greast of 1.a1,2.a2,....2

sekara0809

a1,a2,...a2007 are 1,2,.....2007 in same order. if 'x' is the greast of 1.a1,2.a2,....2007.a2007, prove that x >=(1004)^2.

How?

sandeepramesh

Note by the rearrangement theorem or greedy algorithm the maximum maximum is 2007*2007 when the two sequences are similarly sorted and the minimum maximum is when the two sequences are oppositely sorted. so the minimum maximum is 104*104 so the max >=(104)^2

RyuAmakusa

i think my interpretation of the q must be wrong tell if i am correct

x is the max of 1.1,2.2,3.3,.........2007.2007
because thq q says"a1,a2,...a2007 are 1,2,.....2007 in same order"
in the same order means a1 =1,a2=2,...
hear obviously x should
be 2007.2007 now (2007)^2 > (1004)^2 whats there to prove.

sandeepramesh

i think to satisfy the question we must assume that he made a typo. It must be 'some' order and not 'same' order. With this assumption, i proceeded with the question.

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