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Problems
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National and Regional Contests
China Contests
China National Olympiad
2023 China National Olympiad
4
4
Part of
2023 China National Olympiad
Problems
(1)
China MO 2023 P4
Source: China MO 2023 P4
12/30/2022
Find the minimum positive integer
n
≥
3
n\ge 3
n
≥
3
, such that there exist
n
n
n
points
A
1
,
A
2
,
⋯
,
A
n
A_1,A_2,\cdots, A_n
A
1
,
A
2
,
⋯
,
A
n
satisfying no three points are collinear and for any
1
≤
i
≤
n
1\le i\le n
1
≤
i
≤
n
, there exist
1
≤
j
≤
n
(
j
≠
i
)
1\le j \le n (j\neq i)
1
≤
j
≤
n
(
j
=
i
)
, segment
A
j
A
j
+
1
A_jA_{j+1}
A
j
A
j
+
1
pass through the midpoint of segment
A
i
A
i
+
1
A_iA_{i+1}
A
i
A
i
+
1
, where
A
n
+
1
=
A
1
A_{n+1}=A_1
A
n
+
1
=
A
1
combinatorics