## Search found 37 matches

Tue Jun 13, 2017 9:38 pm
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 17519

### Re: Beginner's Marathon

$Solution to Problem 21$ Let $a_1 < a_2 < a_3 < a_4$. Then, $(a_3+a_4)$ can't divide $(a_1+a_2)$ and $(a_2+a_4)$ can't divide $(a_1+a_3)$. So, $n_A$ < 4. So, to get the max value 4, $(a_1+a_3)|(a_2+a_4)$, $(a_1+a_2)|(a_3+a_4)$, $(a_1+a_4)|(a_2+a_3)$ and $(a_2+a_3)|(a_1+a_4)$. So, $a_1+a_4 = a_2+a_3$...
Wed Jun 07, 2017 9:23 pm
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 17519

### Re: Beginner's Marathon

Problem $19$:

If $127$ people play in a singles tennis tournament, prove that at the end of the tournament, the number of people who have played an odd number of games is even.
Wed Jun 07, 2017 9:11 pm
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 17519

### Re: Beginner's Marathon

Solution to Problem $18$: The $21$ answer the host received were different. Then all the handshake numbers occur from $0$ to $20$. Let's name the people according to their handshake number -- $H_0, H_1,....,H_{20}$. Here, $H_0$ shakes hands with no one. And $H_{20}$ shakes hands with everyone except...
Sun Apr 23, 2017 11:49 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia #2
Replies: 30
Views: 25695

### Re: BDMO Forum Mafia #2

Thamim Zahin wrote:I am not voting myself because I am gonju
So, if no one else come forward to declare themselves 'gonju', we can declare thamimzahin 'gonju'.
Thu Apr 20, 2017 9:08 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia #2
Replies: 30
Views: 25695

### Re: BDMO Forum Mafia #2

Take a preliminary vote?
Tis the first day phase and we have no info, so maybe a vote will help.
Wed Apr 19, 2017 12:29 am
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 17519

### Re: Beginner's Marathon

As the ants are arbitrary, when they collide and move in opposite directions, basically nothing changes. For example, let's name them A and B. A was going right and B left. When they collide, they change directions, so A goes left and B goes right. But as the ants are similar, we can just take it, t...
Mon Apr 17, 2017 11:51 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia #2
Replies: 30
Views: 25695

### Re: BDMO Forum Mafia #2

Can you please elaborate the role of the projective preist?
Tue Apr 11, 2017 9:41 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia #2
Replies: 30
Views: 25695

### Re: BDMO Forum Mafia #2

Oka, I am in too.
Sat Apr 08, 2017 11:01 am
Forum: Junior Level
Topic: Beginner's Marathon
Replies: 68
Views: 17519

### Re: Beginner's Marathon

Problem 10.
Let $S$ be a square of side $2$, and choose $9$ points inside $S$. Show that $3$ of these points may be chosen which are the vertices of a triangle of area $\leq \dfrac{1}{2}$.

Btw, this is a really easy problem and please participate, everyone.
Tue Apr 04, 2017 12:23 am
Forum: Social Lounge
Topic: BDMO Forum Mafia #1
Replies: 52
Views: 21277

### Re: BDMO Forum Mafia #1

Dshasan is agreeing with anyone and everyone. Doesn't his attempts seem like a desperate man's last chance to save his life? Just watch the game and see how many times he has changed his opinion.

So, I am voting dshasan.

VOTE: (dshasan)