Search found 151 matches

by Avik Roy
Mon Mar 28, 2011 8:26 pm
Forum: Higher Secondary Level
Topic: minimum products needed
Replies: 0
Views: 1019

minimum products needed

Consider a sequence of $n$ nonzero numbers where at least one of them is positive. You are not allowed to see the numbers, but can know the sign of product of any two. Find, with proof, the minimum number of products you need to know if you want to determine the sign of every number in that sequence.
by Avik Roy
Wed Mar 23, 2011 12:27 am
Forum: College / University Level
Topic: Injection from R2 to R
Replies: 4
Views: 6279

Re: Injection from R2 to R

There's one that maps all the points in $(0,1) \times (0,1)$ to $(0,1)$. Take $(0.a_1a_2a_3 ... ,0.b_1b_2b_3 ...) \rightarrow 0.a_1b_1a_2b_2a_3b_3...$. Such a map should work also
by Avik Roy
Tue Feb 15, 2011 11:19 pm
Forum: Physics
Topic: simple pendulam in vacuam
Replies: 3
Views: 1749

Re: simple pendulam in vacuam

Motion of a simple pendulum is governed by gravity. So there is no reason that it will not oscillate in vacuum
by Avik Roy
Mon Feb 14, 2011 2:16 pm
Forum: Number Theory
Topic: An easy to prove result about squares
Replies: 1
Views: 1133

An easy to prove result about squares

There are infinitely many non palidromic squares so that their digit-inverse (number formed by reading the number right to left) is also a square.

The result is wordy but the proof is verrrrry easy :)
by Avik Roy
Sun Feb 13, 2011 11:45 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Secondary (Higher Secondary) 2011/7
Replies: 8
Views: 3648

Re: BdMO National Secondary (Higher Secondary) 2011/7

Fahim, your strange proof is correct.
However, you should note one thing here (though I'm sure you are just good enough at recognizing it). For the completeness of the proof, you should also prove that friend of enemy and enemy of friend is an enemy. It seems trivial, but necessary.
by Avik Roy
Sun Feb 13, 2011 6:09 pm
Forum: Social Lounge
Topic: Math Books in Ekushey Boi Mela
Replies: 4
Views: 2024

Re: Math Books in Ekushey Boi Mela

The fair opens at 3 pm
by Avik Roy
Sun Feb 13, 2011 9:04 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Secondary (Higher Secondary) 2011/6
Replies: 7
Views: 3175

Re: BdMO National Secondary (Higher Secondary) 2011/6

Fahim, Well done. Your proof is correct.
by Avik Roy
Sat Feb 12, 2011 11:45 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Secondary (Higher Secondary) 2011/6
Replies: 7
Views: 3175

Re: BdMO National Secondary (Higher Secondary) 2011/6

Once upon a time, there lived a man called Euclid in a beautiful country called Greece, who proved that there are infinitely many primes
by Avik Roy
Sat Feb 12, 2011 11:41 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2011/10
Replies: 3
Views: 2077

Re: BdMO National Higher Secondary 2011/10

There's a note about this problem-
This was one of the earliest problems of the question camp (might be even the first one). I like this problem very much, it is a beautiful one. One who solves it should appreciate its elegance as well.
by Avik Roy
Sat Feb 05, 2011 10:43 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO 2011 National: Are you ready?
Replies: 8
Views: 2828

Re: Preparation for BdMO 2011 National

১) মাথা ঠাণ্ডা রাখ
২) মাথা ঠাণ্ডা রাখ
৩) মাথা ঠাণ্ডা রাখ
৪) কিছু প্র্যাকটিস কর
৫) পারলে আরো কিছু প্র্যাকটিস কর