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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2019 India PRMO
30
Set / Equal Sums
Set / Equal Sums
Source:
August 11, 2019
Sets
sums
Problem Statement
Let
E
E
E
denote the set of all natural numbers
n
n
n
such that
3
<
n
<
100
3 < n < 100
3
<
n
<
100
and the set
{
1
,
2
,
3
,
…
,
n
}
\{ 1, 2, 3, \ldots , n\}
{
1
,
2
,
3
,
…
,
n
}
can be partitioned in to
3
3
3
subsets with equal sums. Find the number of elements of
E
E
E
.
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