MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2017 Harvard-MIT Mathematics Tournament
11
2017 Guts #11: Partition of 3-space
2017 Guts #11: Partition of 3-space
Source:
February 21, 2017
geometry
Problem Statement
Consider the graph in
3
3
3
-space of
0
=
x
y
z
(
x
+
y
)
(
y
+
z
)
(
z
+
x
)
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
.
0 = xyz(x + y)(y + z)(z + x)(x - y)(y - z)(z - x).
0
=
x
yz
(
x
+
y
)
(
y
+
z
)
(
z
+
x
)
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
.
This graph divides
3
3
3
-space into
N
N
N
connected regions. What is
N
N
N
?
Back to Problems
View on AoPS