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South African Mathematics Olympiad Difficulty 4.1 AIME Find the answer South Africa
Calculate 2015 − ( 2015 − ( 2015 − ( 2015 − 1 ) ) ) 2015 - (2015 - (2015 - (2015 - 1))) 2015 − ( 2015 − ( 2015 − ( 2015 − 1 )))
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A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.
Solution 2015 − ( 2015 − ( 2015 − ( 2015 − 1 ) ) ) = 2015 − ( 2015 − ( 2015 − 2014 ) ) = 2015 − ( 2015 − 1 ) = 2015 − 2014 = 1. 2015 - (2015 - (2015 - (2015 - 1))) = 2015 - (2015 - (2015 - 2014)) = 2015 - (2015 - 1) = 2015 - 2014 = 1. 2015 − ( 2015 − ( 2015 − ( 2015 − 1 ))) = 2015 − ( 2015 − ( 2015 − 2014 )) = 2015 − ( 2015 − 1 ) = 2015 − 2014 = 1.
Alternatively,2015 − ( 2015 − ( 2015 − ( 2015 − 1 ) ) ) = 2015 − 2015 + 2015 − 2015 + 1 = 1. 2015 - (2015 - (2015 - (2015 - 1))) = 2015 - 2015 + 2015 - 2015 + 1 = 1. 2015 − ( 2015 − ( 2015 − ( 2015 − 1 ))) = 2015 − 2015 + 2015 − 2015 + 1 = 1.
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