MathDB
Problems
Contests
Undergraduate contests
Putnam
1956 Putnam
A5
A5
Part of
1956 Putnam
Problems
(1)
Putnam 1956 A5
Source: Putnam 1956
7/5/2022
Call a subset of
{
1
,
2
,
…
,
n
}
\{1,2,\ldots, n\}
{
1
,
2
,
…
,
n
}
unfriendly if no two of its elements are consecutive. Show that the number of unfriendly subsets with
k
k
k
elements is
(
n
−
k
+
1
k
)
.
\binom{n-k+1}{k}.
(
k
n
−
k
+
1
)
.
Putnam
binomial coefficients
combinatorics