Smallest Sum Absolutes

Level 2

What is the largest integer N N such that x 3 + 2 x 3 + 3 x 3 + + 333 x 3 > N \mid x-3 \mid + \mid 2x - 3 \mid + \mid 3x - 3 \mid + \ldots + \mid 333x - 3 \mid > N for all real x x ?


The answer is 412.

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