MathDB
Problems
Contests
National and Regional Contests
Hong Kong Contests
Hong Kong National Olympiad
2006 Hong kong National Olympiad
1
1
Part of
2006 Hong kong National Olympiad
Problems
(1)
Any three elements of a subset
Source:
11/9/2010
A subset
M
M
M
of
{
1
,
2
,
.
.
.
,
2006
}
\{1, 2, . . . , 2006\}
{
1
,
2
,
...
,
2006
}
has the property that for any three elements
x
,
y
,
z
x, y, z
x
,
y
,
z
of
M
M
M
with
x
<
y
<
z
x < y < z
x
<
y
<
z
,
x
+
y
x+ y
x
+
y
does not divide
z
z
z
. Determine the largest possible size of
M
M
M
.
combinatorics
Ramsey Theory
Schur