2017-dimensional volume?!

Geometry Level 4

Let S S be the set of all points ( x 1 , x 2 , x 3 , , x 2017 ) (x_1, x_2, x_3, \ldots, x_{2017}) in R 2017 \mathbb{R}^{2017} satisfying x i + x j 1 |x_i|+|x_j | \leq 1 for any 1 i < j 2017 1 \leq i < j \leq 2017 . The hypervolume (in 2017 2017 dimensions) of S S can be expressed as m n \frac{m}{n} , where m m and n n are relatively prime positive integers. Find 100 m + n 100m + n .


The answer is 201.

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