MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Polish MO Finals
2016 Polish MO Finals
3
Combinatorics
Combinatorics
Source: Polish Mathematical Olympiad 2016 P3- Final Round
April 8, 2016
combinatorics
counting
Problem Statement
Let
a
,
b
∈
Z
+
a, \ b \in \mathbb{Z_{+}}
a
,
b
∈
Z
+
. Denote
f
(
a
,
b
)
f(a, b)
f
(
a
,
b
)
the number sequences
s
1
,
s
2
,
.
.
.
,
s
a
s_1, \ s_2, \ ..., \ s_a
s
1
,
s
2
,
...
,
s
a
,
s
i
∈
Z
s_i \in \mathbb{Z}
s
i
∈
Z
such that
∣
s
1
∣
+
∣
s
2
∣
+
.
.
.
+
∣
s
a
∣
≤
b
|s_1|+|s_2|+...+|s_a| \le b
∣
s
1
∣
+
∣
s
2
∣
+
...
+
∣
s
a
∣
≤
b
. Show that
f
(
a
,
b
)
=
f
(
b
,
a
)
f(a, b)=f(b, a)
f
(
a
,
b
)
=
f
(
b
,
a
)
.
Back to Problems
View on AoPS