Let $n$ be a fixed positive odd integer. Take $m+2$ distinct points $P_0,P_1,\ldots ,P_{m+1}$ (where $m$ is a non-negative integer) on the coordinate plane in such a way that the following three conditions are satisfied:
1) $P_0=(0,1),P_{m+1}=(n+1,n)$, and for each integer $i,1\le i\le m$, both $x$- and $y$- coordinates of $P_i$ are integers lying in between $1$ and $n$ ($1$ and $n$ inclusive).
2) For each integer $i,0\le i\le m$, $P_iP_{i+1}$ is parallel to the $x$-axis if $i$ is even, and is parallel to the $y$-axis if $i$ is odd.
3) For each pair $i,j$ with $0\le i<j\le m$, line segments $P_iP_{i+1}$ and $P_jP_{j+1}$ share at most $1$ point.
Determine the maximum possible value that $m$ can take.
APMO 2011 Problem 4
Discussion on Asian Pacific Mathematical Olympiad (APMO)
-
- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Unread post by samiul_samin » Thu Jan 10, 2019 11:37 pm
Return to “Asian Pacific Math Olympiad (APMO)”
Jump to
- General Discussion
- ↳ News / Announcements
- ↳ Introductions
- ↳ Social Lounge
- ↳ Site Support
- ↳ Test Forum
- ↳ Teachers' and Parents' Forum
- Mathematics
- ↳ Primary Level
- ↳ Junior Level
- ↳ Secondary Level
- ↳ Higher Secondary Level
- ↳ College / University Level
- Olympiads & Other Programs
- ↳ Divisional Math Olympiad
- ↳ Primary: Solved
- ↳ Junior: Solved
- ↳ Secondary: Solved
- ↳ H. Secondary: Solved
- ↳ National Math Olympiad (BdMO)
- ↳ National Math Camp
- ↳ Asian Pacific Math Olympiad (APMO)
- ↳ International Olympiad in Informatics (IOI)
- ↳ International Mathematical Olympiad (IMO)
- Olympiad Level
- ↳ Geometry
- ↳ Number Theory
- ↳ Algebra
- ↳ Combinatorics
- Sciences
- ↳ Physics
- ↳ Chemistry
- ↳ Computer Science
- ↳ Biology
- ↳ Astronomy & Astrophysics