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Problems
Contests
National and Regional Contests
The Philippines Contests
Philippine MO
2008 Philippine MO
1
1
Part of
2008 Philippine MO
Problems
(1)
Disjoint Subsets with Same Sum
Source: 2008 Philippine Mathematical Olympiad Problem 1
5/6/2014
Prove that the set
{
1
,
2
,
⋯
,
2007
}
\{1, 2, \cdots, 2007\}
{
1
,
2
,
⋯
,
2007
}
can be expressed as the union of disjoint subsets
A
i
A_i
A
i
for
i
=
1
,
2
,
⋯
,
223
i=1,2,\cdots, 223
i
=
1
,
2
,
⋯
,
223
such that each
A
i
A_i
A
i
contains nine elements and the sum of all the elements in each
A
i
A_i
A
i
is the same.
combinatorics