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National and Regional Contests
PEN Problems
PEN O Problems
54
54
Part of
PEN O Problems
Problems
(1)
O 54
Source:
5/25/2007
Let
S
S
S
be a subset of
{
1
,
2
,
3
,
⋯
,
1989
}
\{1, 2, 3, \cdots, 1989 \}
{
1
,
2
,
3
,
⋯
,
1989
}
in which no two members differ by exactly
4
4
4
or by exactly
7
7
7
. What is the largest number of elements
S
S
S
can have?
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