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50th Mathematical Olympiad in Ukraine, Third Round (January 23, 2010)

Ukraine 2010 algebra

Problem

In the expression there are somehow placed brackets and the value is calculated. Find the maximum value that can be reached. Justify your answer.

Notice. Left bracket can be placed only before a number and right - only after. For example, expressions and are incorrect.
Solution


Consider an arbitrary arrangement of the brackets. Numbers and always have signs '+' and '-', respectively, that's why the sum reaches the maximum value when the other terms will have '+' sign.
Final answer
56

Techniques

Integers