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Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
1995 India National Olympiad
3
No. of subsets
No. of subsets
Source: INMO 1995 Problem 3
October 6, 2005
symmetry
combinatorics unsolved
combinatorics
Problem Statement
Show that the number of
3
−
3-
3
−
element subsets
{
a
,
b
,
c
}
\{ a , b, c \}
{
a
,
b
,
c
}
of
{
1
,
2
,
3
,
…
,
63
}
\{ 1 , 2, 3, \ldots, 63 \}
{
1
,
2
,
3
,
…
,
63
}
with
a
+
b
+
c
<
95
a+b +c < 95
a
+
b
+
c
<
95
is less than the number of those with
a
+
b
+
c
≥
95.
a + b +c \geq 95.
a
+
b
+
c
≥
95.
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