Search found 90 matches

by Zawadx
Mon Mar 27, 2017 8:14 pm
Forum: Divisional Math Olympiad
Topic: BDMO REGIONAL 2015
Replies: 5
Views: 1850

Re: BDMO REGIONAL 2015

2 , 118 AND 8 You do have a point xD The question is not properly stated. A better question would be 'Upto how many numbers must the sequence $2,3,8,13,18,23, \dots ,118$ be continued to ensure that there exists at least one pair with sum $126$'. Though that is still not perfect because the sequenc...
by Zawadx
Mon Mar 27, 2017 2:38 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia #1
Replies: 52
Views: 8489

BDMO Forum Mafia #1

https://s-media-cache-ak0.pinimg.com/originals/3d/3c/2d/3d3c2df029a79ab5ae6550b40d5006e8.jpg Guide to mafia: Mafia is generally played between two teams: Civilians and Mafia. The civilians are the main group, and they enjoy the advantage of being a majority. Every day, the civilians post in the thr...
by Zawadx
Fri Mar 24, 2017 12:00 am
Forum: Site Support
Topic: The Gonit IshCool Project
Replies: 3
Views: 1246

Re: The Gonit IshCool Project

Why do you think a chat system is essential for learning? Real-time chats are quick and easy, but they can get messy sometimes and might make it harder to get the point across. Often it's better to take the time to think and type a proper response without the pressure of real time. My plan was that ...
by Zawadx
Thu Mar 23, 2017 12:27 am
Forum: Algebra
Topic: f(x)=?
Replies: 1
Views: 625

Re: f(x)=?

This can be solved by the basic arguments used to solve Cauchy's FE over Q. Try it yourself!

Hint if you're extremely desperate:
$$ f( n + \frac{1}{m}) = n + f( \frac{1}{m} ) $$
by Zawadx
Thu Mar 23, 2017 12:14 am
Forum: Site Support
Topic: The Gonit IshCool Project
Replies: 3
Views: 1246

The Gonit IshCool Project

((Posting this to site support since it's the only sub-forum with a topic close to meta discussion ._.)) This is a project I thought up about a month ago, as a way to teach people specific topics in problem solving which can't be traditionally learned. For example, functional equations aren't really...
by Zawadx
Wed Mar 22, 2017 11:47 pm
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 11184

Re: Beginner's Marathon

$\text{Problem} 1$ NASA has proposed populating Mars with 2,004 settlements. The only way to get from one settlement to another will be by a connecting tunnel. A bored bureaucrat draws on a map of Mars, randomly placing N tunnels connecting the settlements in such a way that no two settlements have ...
by Zawadx
Wed Mar 22, 2017 11:24 pm
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 11184

Beginner's Marathon

Too much of the forum is dedicated to advanced problem solving, which I'm afraid is a level accessible to only a few in the country. Let's change that, shall we? This thread is dedicated for a marathon on relatively easy problems. The rules are similar to the Geo Marathon or the Combi Marathon , jus...
by Zawadx
Wed Mar 22, 2017 11:06 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia
Replies: 5
Views: 1349

BDMO Forum Mafia

Since Mafia was a big hit at this camp, we could perhaps continue that tradition in a more open manner through forum Mafia. For those who are new to the game, here's a short guide I wrote ages ago: Mafia is generally played between two teams: Civilians and Mafia. The civilians are the main group, an...
by Zawadx
Wed Mar 01, 2017 8:57 pm
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 8514

Re: Combi Marathon

$\text{Problem 15}$ You and your sister have inherited a necklace, which is a linear string of $n$ different types of gemstones with an even number of stones of each type. You want to cut the necklace at some points so that you may distribute the pieces to yourself and your sister with everyone gett...
by Zawadx
Wed Mar 01, 2017 8:51 pm
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 8514

Re: Combi Marathon

Well that was pretty easy $\text{Solution to Problem 14}$ We prove that at most $2^n-1$ moves are required by, you guessed it, induction. We follow the problem's definition for $k$ and $h$. We denote the label of the card on cell $i$ by $c(i)$ Lemma 0 : For all cells $i$ with $i<h$, $c(i)=i$. Since ...