MathDB
Problems
Contests
Undergraduate contests
Putnam
1993 Putnam
A3
A3
Part of
1993 Putnam
Problems
(1)
Putnam 1993 A3
Source: 1993 Putnam
10/26/2020
Let
P
P
P
be the set of all subsets of
1
,
2
,
.
.
.
,
n
{1, 2, ... , n}
1
,
2
,
...
,
n
. Show that there are
1
n
+
2
n
+
.
.
.
+
m
n
1^n + 2^n + ... + m^n
1
n
+
2
n
+
...
+
m
n
functions
f
:
P
⟼
1
,
2
,
.
.
.
,
m
f : P \longmapsto {1, 2, ... , m}
f
:
P
⟼
1
,
2
,
...
,
m
such that
f
(
A
∩
B
)
=
m
i
n
(
f
(
A
)
,
f
(
B
)
)
f(A \cap B) = min( f(A), f(B))
f
(
A
∩
B
)
=
min
(
f
(
A
)
,
f
(
B
))
for all
A
,
B
.
A, B.
A
,
B
.
Putnam
combinatorics