# Six real numbers

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• Aug 20th 2011, 11:22 PM
alexmahone
Six real numbers
A computer programmer claims that he generated six real numbers $a_1, a_2, \cdots, a_6$ so that the sum of any four consecutive $a_i$'s is positive, but the sum of any 3 consecutive $a_i$'s is negative. Prove that his claim is false.
• Aug 20th 2011, 11:35 PM
alexmahone
Re: Six real numbers
I think I got it.

a1+a2+a3<0 and a1+a2+a3+a4>0
imply a4>0
Similarly a5>0 and a6>0

a4+a5+a6>0 (Contradiction)