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Putnam
1973 Putnam
B1
B1
Part of
1973 Putnam
Problems
(1)
Putnam 1973 B1
Source: Putnam 1973
5/29/2022
Let
a
1
,
a
2
,
…
a
2
n
+
1
a_1, a_2, \ldots a_{2n+1}
a
1
,
a
2
,
…
a
2
n
+
1
be a set of integers such that, if any one of them is removed, the remaining ones can be divided into two sets of
n
n
n
integers with equal sums. Prove
a
1
=
a
2
=
⋯
=
a
2
n
+
1
.
a_{1}=a_2 =\cdots=a_{2n+1}.
a
1
=
a
2
=
⋯
=
a
2
n
+
1
.
Putnam
Integers