Search found 181 matches
- Thu Apr 20, 2017 10:03 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 44447
Re: Beginner's Marathon
I think you should give the full solution to the problems or give hints if the thread is stuck for some days.
- Thu Apr 20, 2017 8:24 pm
- Forum: Social Lounge
- Topic: BDMO Forum Mafia #2
- Replies: 30
- Views: 47640
Re: BDMO Forum Mafia #2
Okay, guys. Would you want to take a preliminary vote to get some information? Or do you want to discuss about what might be our best strategy?
Re: A Lemma?
I think you have the wrong idea of elegance. To see what not elegant is, Thanic Nur Samin vaiya is your best choice.
- Wed Apr 12, 2017 8:22 pm
- Forum: Combinatorics
- Topic: Another Ah moment
- Replies: 1
- Views: 5264
Re: Another Ah moment
No one tried this problem. Me very sad.
- Wed Apr 12, 2017 7:14 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO 2017 junior/4
- Replies: 11
- Views: 7898
Re: BdMO 2017 junior/4
So basically you do different cases on the primes dividing $n^2$ or $n-1$. And these cases yield different divisibility conditions. And CRT is the method to find the smallest number that suppression every congruence in a system. Look it up. The notation might be scary but it's quite natural and intu...
- Wed Apr 12, 2017 1:29 am
- Forum: Combinatorics
- Topic: Another Ah moment
- Replies: 1
- Views: 5264
Another Ah moment
You are given a TV screen with $n×(n+2)$ pixels(the dimension is $n $ on a side and $n+2$ on another side). Initially, there are $k $ pixels turned on. In any $2×2$ screen, as soon as there are $3$ unit screens which are off, you can turn off the $4$th screen. Your goal is to turn the whole TV off. ...
- Tue Apr 11, 2017 10:30 pm
- Forum: Combinatorics
- Topic: Combi Marathon
- Replies: 48
- Views: 44024
Re: Combi Marathon
Solution? And another problem please.
- Tue Apr 11, 2017 4:55 pm
- Forum: Social Lounge
- Topic: BDMO Forum Mafia #2
- Replies: 30
- Views: 47640
Re: BDMO Forum Mafia #2
"Everyone's super is another way to say no one is."Zawadx wrote:
This time, EVERYONE will get a special power role (no vanillas). Hopefully this will result in some fun for everyone!
.
BTW, I'm playing.
- Tue Apr 11, 2017 4:21 pm
- Forum: Combinatorics
- Topic: বিয়ে
- Replies: 6
- Views: 14787
বিয়ে
You are given a $10$*$10$ grid with the property that in every row, exactly three squares are shaded, and in every column, exactly 3 squares are shaded. Prove that you can select 10 if these shaded squares so that each of them are in different rows and columns.
- Mon Apr 10, 2017 12:45 pm
- Forum: Junior Level
- Topic: Beginner's Marathon
- Replies: 68
- Views: 44447
Re: Beginner's Marathon
Problem $11$
For a positive integer $n$, let $f(n)$ denote the greatest odd divisor of $n$. Prove that for any integer $x$, $f(x+1)+f(x+2)+........f(2x) = x^2$.
For a positive integer $n$, let $f(n)$ denote the greatest odd divisor of $n$. Prove that for any integer $x$, $f(x+1)+f(x+2)+........f(2x) = x^2$.