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Putnam
2017 Putnam
B6
Putnam 2017 B6
Putnam 2017 B6
Source:
December 3, 2017
Putnam
Putnam 2017
Problem Statement
Find the number of ordered
64
64
64
-tuples
{
x
0
,
x
1
,
…
,
x
63
}
\{x_0,x_1,\dots,x_{63}\}
{
x
0
,
x
1
,
…
,
x
63
}
such that
x
0
,
x
1
,
…
,
x
63
x_0,x_1,\dots,x_{63}
x
0
,
x
1
,
…
,
x
63
are distinct elements of
{
1
,
2
,
…
,
2017
}
\{1,2,\dots,2017\}
{
1
,
2
,
…
,
2017
}
and
x
0
+
x
1
+
2
x
2
+
3
x
3
+
⋯
+
63
x
63
x_0+x_1+2x_2+3x_3+\cdots+63x_{63}
x
0
+
x
1
+
2
x
2
+
3
x
3
+
⋯
+
63
x
63
is divisible by
2017.
2017.
2017.
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