MathDB
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National and Regional Contests
India Contests
India IOQM
2023-24 IOQM India
21
IOQM 2023-24 P-21
IOQM 2023-24 P-21
Source:
September 3, 2023
function
Problem Statement
For
n
∈
N
n \in \mathbb{N}
n
∈
N
, consider non-negative valued functions
f
f
f
on
{
1
,
2
,
⋯
,
n
}
\{1,2, \cdots , n\}
{
1
,
2
,
⋯
,
n
}
satisfying
f
(
i
)
⩾
f
(
j
)
f(i) \geqslant f(j)
f
(
i
)
⩾
f
(
j
)
for
i
>
j
i>j
i
>
j
and
∑
i
=
1
n
(
i
+
f
(
i
)
)
=
2023.
\sum_{i=1}^{n} (i+ f(i))=2023.
∑
i
=
1
n
(
i
+
f
(
i
))
=
2023.
Choose
n
n
n
such that
∑
i
=
1
n
f
(
i
)
\sum_{i=1}^{n} f(i)
∑
i
=
1
n
f
(
i
)
is at least. How many such functions exist in that case?
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