https://code.google.com/codejam/contest/32016/dashboard#s=p0

I'm solving this problem and found a solution but I can't prove my solution's 
correctness. Is there anyone can prove this?

My solution is below:

1. Sort two vectors. Two vectors becomes (x1, ..., xn), (y1, ..., yn)
2. Minimum product is x1 yn + x2 yn-1 + ... + xn y1

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