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Discussion of Problem 1522. Factory

I'm so enchanted to the problem. It's amazing
Posted by Marshall Mathers 20 May 2011 12:38
The process to prove it  is both easy and creative.
Sort all the numbers in the following way:

^
|a<c: sort them according to its value of A+B in increasing order
|
|a=c: you may sort them arbitrarily
|
|a>c: sort them according to its value of B+C in decreasing order
|