An anti-Pascal triangle is an equilateral triangular array of numbers such that, except for the numbers in the bottom row, each number is the absolute value of the difference of the two numbers immediately below it. For example, the following is an anti-Pascal triangle with four rows which contains every integer from $1$ to $10$.
\[4\]
\[2 \ \ 6\]
\[5 \ \ 7 \ \ 1 \]
\[8 \ \ 3 \ \ 10 \ \ 9 \]
Does there exist an anti-Pascal triangle with $2018$ rows which contains every integer from $1$ to $1 + 2 + 3 + \dots + 2018$?
IMO 2018 P3
Discussion on International Mathematical Olympiad (IMO)
-
- Posts:16
- Joined:Wed Aug 10, 2016 1:29 am
Unread post by M Ahsan Al Mahir » Wed Jan 09, 2019 11:46 pm
Return to “International Mathematical Olympiad (IMO)”
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