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MathNet 2017-part-07 — 172 problems (EN–VI) Question 36

Math Olympiad Vault · MathNet 2017-part-07 — 172 problems (EN–VI)

Question 36

Consider the graph in 3-space of
$$
0 = x y z (x + y)(y + z)(z + x)(x - y)(y - z)(z - x)
$$

This graph divides 3-space into $N$ connected regions. What is $N$?