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2013 Harvard-MIT Mathematics Tournament
27
27
Part of
2013 Harvard-MIT Mathematics Tournament
Problems
(1)
2013 HMMT Guts #27: Intersection of Hypercube and Hyperplane
Source:
3/26/2013
Let
W
W
W
be the hypercube
{
(
x
1
,
x
2
,
x
3
,
x
4
)
∣
0
≤
x
1
,
x
2
,
x
3
,
x
4
≤
1
}
\{(x_1,x_2,x_3,x_4)\,|\,0\leq x_1,x_2,x_3,x_4\leq 1\}
{(
x
1
,
x
2
,
x
3
,
x
4
)
∣
0
≤
x
1
,
x
2
,
x
3
,
x
4
≤
1
}
. The intersection of
W
W
W
and a hyperplane parallel to
x
1
+
x
2
+
x
3
+
x
4
=
0
x_1+x_2+x_3+x_4=0
x
1
+
x
2
+
x
3
+
x
4
=
0
is a non-degenerate
3
3
3
-dimensional polyhedron. What is the maximum number of faces of this polyhedron?
HMMT