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Contests
National and Regional Contests
South Africa Contests
South Africa National Olympiad
2006 South africa National Olympiad
5
5
Part of
2006 South africa National Olympiad
Problems
(1)
Subsets without consecutive elements
Source: South African MO 2006 Q5
5/27/2012
Find the number of subsets
X
X
X
of
{
1
,
2
,
…
,
10
}
\{1,2,\dots,10\}
{
1
,
2
,
…
,
10
}
such that
X
X
X
contains at least two elements and such that no two elements of
X
X
X
differ by
1
1
1
.
Pascal's Triangle
combinatorics unsolved
combinatorics