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Algebra Difficulty 4.1 AIME Find the answer South Africa

Calculate 2015(2015(2015(20151)))2015 - (2015 - (2015 - (2015 - 1))).

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

2015(2015(2015(20151)))=2015(2015(20152014))=2015(20151)=20152014=1.2015 - (2015 - (2015 - (2015 - 1))) = 2015 - (2015 - (2015 - 2014)) = 2015 - (2015 - 1) = 2015 - 2014 = 1.

Alternatively,
2015(2015(2015(20151)))=20152015+20152015+1=1.2015 - (2015 - (2015 - (2015 - 1))) = 2015 - 2015 + 2015 - 2015 + 1 = 1.

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