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National and Regional Contests
PEN Problems
PEN O Problems
9
9
Part of
PEN O Problems
Problems
(1)
O 9
Source:
5/25/2007
Let
n
n
n
be an integer, and let
X
X
X
be a set of
n
+
2
n+2
n
+
2
integers each of absolute value at most
n
n
n
. Show that there exist three distinct numbers
a
,
b
,
c
ā
X
a, b, c \in X
a
,
b
,
c
ā
X
such that
c
=
a
+
b
c=a+b
c
=
a
+
b
.
pigeonhole principle
induction
absolute value