MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
1999 India National Olympiad
6
6
Part of
1999 India National Olympiad
Problems
(1)
Splitting integers
Source: INMO 1999 Problem 6
10/7/2005
For which positive integer values of
n
n
n
can the set
{
1
,
2
,
3
,
…
,
4
n
}
\{ 1, 2, 3, \ldots, 4n \}
{
1
,
2
,
3
,
…
,
4
n
}
be split into
n
n
n
disjoint
4
4
4
-element subsets
{
a
,
b
,
c
,
d
}
\{ a,b,c,d \}
{
a
,
b
,
c
,
d
}
such that in each of these sets
a
=
b
+
c
+
d
3
a = \dfrac{b +c +d} {3}
a
=
3
b
+
c
+
d
.
number theory solved
number theory