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Contests
National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2016 Switzerland - Final Round
9
9
Part of
2016 Switzerland - Final Round
Problems
(1)
n -element subset F of {1, . . . , 2n}
Source: Switzerland - 2016 Swiss MO Final Round p9
1/14/2023
Let
n
≥
2
n \ge 2
n
≥
2
be a natural number. For an
n
n
n
-element subset
F
F
F
of
{
1
,
.
.
.
,
2
n
}
\{1, . . . , 2n\}
{
1
,
...
,
2
n
}
we define
m
(
F
)
m(F)
m
(
F
)
as the minimum of all
l
c
m
(
x
,
y
)
lcm \,\, (x, y)
l
c
m
(
x
,
y
)
, where
x
x
x
and
y
y
y
are two distinct elements of
F
F
F
. Find the maximum value of
m
(
F
)
m(F)
m
(
F
)
.
combinatorics
LCM
number theory