Search found 230 matches
- Wed Oct 13, 2021 10:21 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2020 P3
- Replies: 3
- Views: 9297
Re: BdMO National Higher Secondary 2020 P3
Ok we can assume that we have a rectangle with length $\frac{1}{2}$ and breadth $0$. The circle that comprises all those rectangles has an area of $\frac{1}{16} \pi$. So, $\frac{1}{a} = 16$. No other rectangle with the given criteria can be outisde this circle.
- Sat Sep 04, 2021 7:56 pm
- Forum: Combinatorics
- Topic: Iranian Combinatorics Olympiad 2021 - Advanced level - Problem 1 - Frogs on the stone
- Replies: 1
- Views: 13773
Re: Iranian Combinatorics Olympiad 2021 - Advanced level - Problem 1 - Frogs on the stone
Let, $k_i$ be the stone on which ith frog was initially sitting on. Let's say all move M times. Then each frog will naturally go from $k_i \to k_i +M$(Mod 23). We can work on (Mod 23) Now if 2 or more frogs sit on the same stone then we will call one(any) of them 'domain' and the rest 'refugees'. (...
- Mon Aug 16, 2021 9:52 pm
- Forum: Geometry
- Topic: The separation theorem
- Replies: 1
- Views: 17058
Re: The separation theorem
Let $A,B, C, D$ be $4$ distinct points on the plane. Every circle going through $A,C$ intersects with every circle going through $B,D$. Prove that $A,B, C, D$ are either concyclic or collinear. Let us assume that there is 4 points that are neither on a line nor on a circle, but has that property. L...
- Thu Jul 15, 2021 7:51 pm
- Forum: Astronomy & Astrophysics
- Topic: Do you believe in possibility of life in other galaxies?
- Replies: 10
- Views: 30035
Re: Do you believe in possibility of life in other galaxies?
Still, we`ve got a chance. We do not know what other galaxies hide from us. Let me remind you there are many of them. So the chance to find the second Earth is rather plausible. I am not saying there is no chance. But if we really want to do it, we first need to find a way to get out of our solar s...
- Sun Jul 04, 2021 10:18 pm
- Forum: Combinatorics
- Topic: IMO SL 2017 C1 (Easy or fakesolve)
- Replies: 2
- Views: 12914
Re: IMO SL 2017 C1 (Easy or fakesolve)
The solution is quite wordy. My combinatorics solutions are always like that. Let us divide $R$ in unit squares. We can color the first square(Bottom left) black and the squares adjacent to white. In this manner, we can create a chessboard with $R$. Now for obvious reasons, the first corner of $R$ i...
- Fri Jun 25, 2021 10:10 am
- Forum: Physics
- Topic: A Comeback Post (Assignment related)
- Replies: 7
- Views: 82710
Re: A Comeback Post (Assignment related)
I am also on the side of $9.8 ms^{-2}$, because if the acceleration is $0$. Then the object is not supposed to move down. But it does move down. So it has acceleration.
- Tue Jun 15, 2021 10:30 pm
- Forum: Number Theory
- Topic: A problem from number theory
- Replies: 1
- Views: 7826
Re: A problem from number theory
What is the maximum power of $2$ which divides $10^{1002} – 4^{501} ?$ $10^{1002}-4^{501} = 2^{1002}5^{1002}-2^{1002}=2^{1002}(5^{1002}-1) = 2^{1002}(5^{501}+1)(5^{501}-1)$ Now in mod $4$, $5^{501}+1 \equiv 2$ So it is a multipe of $2$ but not $4$. In mod $8$ we get, $5^{501}-1 \equiv 5\times (5^2)...
- Sun Jun 13, 2021 8:29 pm
- Forum: Number Theory
- Topic: Cool modular arithmetic prob
- Replies: 3
- Views: 14667
Re: Cool modular arithmetic prob
An infinite series of integers follows the following rule: $a_{n+1}=2a_n +1$ Is there any $a_0$ for which every term of the series will be a prime number? Clearly, the first term of the sequence $a_0$ must be a prime, Now look at the sequence, $a_{n+1}=2a_n+1$ This can be rephrased as $a_{n+1}=2^{n...
- Sun Jun 13, 2021 6:59 am
- Forum: Number Theory
- Topic: Cool modular arithmetic prob
- Replies: 3
- Views: 14667
Re: Cool modular arithmetic prob
An infinite series of integers follows the following rule: $a_{n+1}=2a_n +1$ Is there any $a_0$ for which every term of the series will be a prime number? Clearly, the first term of the sequence $a_0$ must be a prime, Now look at the sequence, $a_{n+1}=2a_n+1$ This can be rephrased as $a_{n+1}=2^{n...
- Wed Jun 02, 2021 12:09 pm
- Forum: National Math Camp
- Topic: Special Problem Marathon
- Replies: 38
- Views: 34461
Re: Special Problem Marathon
Problem: 05 Let $ABC$ be a triangle with circumcentre $O$. The points $D,E,F$ lie in the interiors of the sides $BC,CA,AB$ respectively, such that $DE$ is perpendicular to $CO$ and $DF$ is perpendicular to $BO$. (By interior we mean, for example, that the point $D$ lies on the line $BC$ and $D$ is ...