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National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2009 Hanoi Open Mathematics Competitions
11
11
Part of
2009 Hanoi Open Mathematics Competitions
Problems
(1)
subset of {1,2,..,100} with 48 elements has 11/(a+b) (HOMC 2009 J Q11)
Source:
7/25/2019
Let
A
=
{
1
,
2
,
.
.
.
,
100
}
A = \{1,2,..., 100\}
A
=
{
1
,
2
,
...
,
100
}
and
B
B
B
is a subset of
A
A
A
having
48
48
48
elements. Show that
B
B
B
has two distint elements
x
x
x
and
y
y
y
whose sum is divisible by
11
11
11
.
combinatorics
number theory
divisible