MathDB
Problems
Contests
National and Regional Contests
India Contests
India IOQM
2023-24 IOQM India
18
18
Part of
2023-24 IOQM India
Problems
(1)
IOQM 2023-24 P-18
Source:
9/3/2023
Let
P
\mathcal{P}
P
be a convex polygon with
50
50
50
vertices. A set
F
\mathcal{F}
F
of diagonals of
P
\mathcal{P}
P
is said to be
m
i
n
i
m
a
l
l
y
f
r
i
e
n
d
l
y
minimally friendly
minima
ll
y
f
r
i
e
n
d
l
y
if any diagonal
d
∈
F
d \in \mathcal{F}
d
∈
F
intersects at most one other diagonal in
F
\mathcal{F}
F
at a point interior to
P
.
\mathcal{P}.
P
.
Find the largest possible number of elements in a
minimally friendly
\text{minimally friendly}
minimally friendly
set
F
\mathcal{F}
F
.