MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN O Problems
23
23
Part of
PEN O Problems
Problems
(1)
O 23
Source:
5/25/2007
Let
k
,
m
,
n
k, m, n
k
,
m
,
n
be integers such that
1
<
n
≤
m
−
1
≤
k
1<n\le m-1 \le k
1
<
n
≤
m
−
1
≤
k
. Determine the maximum size of a subset
S
S
S
of the set
{
1
,
2
,
⋯
,
k
}
\{ 1,2, \cdots, k \}
{
1
,
2
,
⋯
,
k
}
such that no
n
n
n
distinct elements of
S
S
S
add up to
m
m
m
.
induction