Relevant problem: http://lightoj.com:81/volume/problem/1010
(Spoiler alert: You'll find an image of a chessboard there that might give this problem away)
Search found 1015 matches
- Fri Jul 29, 2016 12:06 am
- Forum: Secondary Level
- Topic: 2014-national
- Replies: 15
- Views: 11773
- Sun Jan 10, 2016 5:27 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO 1974/1
- Replies: 2
- Views: 3576
Re: IMO 1974/1
Alice, Betty, and Carol took the same series of examinations. There were one grade of A, one grade of B, and one grade of C for each examination, where A;B and C are different positive integers. The final test scores were Alice Betty Carol $20$ $10$ $9$ If Betty placed first in the arithmetic exami...
- Sun Jan 10, 2016 4:34 pm
- Forum: Secondary: Solved
- Topic: Dhaka Secondary 2011/2 (Junior 2011/4)
- Replies: 8
- Views: 13971
Re: Dhaka Secondary 2011/2 (Junior 2011/4)
Perfect even squares = The squares of even numbers.
- Sun Jan 10, 2016 4:31 pm
- Forum: Divisional Math Olympiad
- Topic: Dhaka Regional 2015 Higher Secondary/9 Secondary/9
- Replies: 1
- Views: 2712
- Sun Jan 03, 2016 11:21 am
- Forum: Number Theory
- Topic: A Problem in Number Theory
- Replies: 2
- Views: 3363
- Mon Dec 07, 2015 11:47 pm
- Forum: Introductions
- Topic: Hello math lovers there is someone new in the forum.
- Replies: 1
- Views: 5906
Re: Hello math lovers there is someone new in the forum.
We are very much disheartened to know that! This wasn't supposed to happen. Let me share my experiences. Math camp has always been my second home, and my dream place. Most of my vivid and fascinating memories have originated there. It has given me many things, but above all, a close friend circle. N...
- Mon Dec 07, 2015 11:11 pm
- Forum: Higher Secondary Level
- Topic: Rightmost two digits of 3^999
- Replies: 5
- Views: 8242
Re: Rightmost two digits of 3^999
Hello, welcome to this forum. Please use latex for maths in future. It honestly makes our work a lot easier.
Check this post for a brief introduction to latex: http://www.matholympiad.org.bd/forum/vi ... p?f=25&t=2
Check this post for a brief introduction to latex: http://www.matholympiad.org.bd/forum/vi ... p?f=25&t=2
- Mon Dec 07, 2015 11:10 pm
- Forum: Site Support
- Topic: time of contest
- Replies: 1
- Views: 9200
Re: time of contest
The regional olympiads will be held from 18 December to 29 January. Check Prothom Alo for details.
- Sun Apr 05, 2015 11:43 am
- Forum: Number Theory
- Topic: USA TSTST 2012/3
- Replies: 1
- Views: 3109
USA TSTST 2012/3
A function $f:\mathbb N\to \mathbb N$ satisfies:
1. $\gcd (m,n) =1 \Longrightarrow \gcd (f(m),f(n))=1$
2. $n\leq f(n) \leq n+2012$
Prove, for every prime $p$, $p|f(n)\Longrightarrow p|n$
Remark: $2012$ can be replaced by any nonnegative integer constant.
1. $\gcd (m,n) =1 \Longrightarrow \gcd (f(m),f(n))=1$
2. $n\leq f(n) \leq n+2012$
Prove, for every prime $p$, $p|f(n)\Longrightarrow p|n$
Remark: $2012$ can be replaced by any nonnegative integer constant.
- Wed Mar 11, 2015 9:49 am
- Forum: Higher Secondary Level
- Topic: Need help
- Replies: 3
- Views: 4053
Re: Need help
AM-GM inequality: For positive real numbers $a_1, a_2,\cdots ,a_n$, we have\[AM=\frac{a_1+a_2+\cdots+a_n}n\ge \sqrt[n]{a_1a_2\cdots a_n}=GM\]with equality when $a_1=a_2=\cdots=a_n$ So, for your problem, let the numbers are $a_1,...,a_n$ and suppose $M=a_1+a_2+\cdots+a_n$. We'll get $\dfrac M n\ge \...