Can we use any Idea of symmetry here?Anindya Biswas wrote: ↑Sun Apr 11, 2021 9:03 pmLet $u$ and $v$ be real numbers. The minimum value of \[\sqrt{u^2+v^2}+\sqrt{(u-1)^2+v^2}+\sqrt{u^2+(v-1)^2}+\sqrt{(u-1)^2+(v-1)^2}\] can be written as $n\sqrt{n}$. Find the value of $10n$.
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- Sun Apr 11, 2021 10:12 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Higher Secondary Problem 2
- Replies: 3
- Views: 3566
Re: BdMO National 2021 Higher Secondary Problem 2
- Sun Apr 11, 2021 10:07 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Higher Secondary Problem 1
- Replies: 2
- Views: 5520
Re: BdMO National 2021 Higher Secondary Problem 1
For a positive integer $n$, let $A(n)$ be equal to the remainder when $n$ is divided by $11$ and let $T(n)=A(1)+A(2)+A(3)+\dots+A(n)$. Find the value of $A(T(2021))$. Note: All the equivalent relations will be modulo 11. We notice $A(n) \equiv n$ and thus $T(n) \equiv \frac{n(n+1)}{2}$ So, $T(2021)...
- Sun Apr 11, 2021 9:38 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Secondary Problem 12
- Replies: 3
- Views: 5047
BdMO National 2021 Secondary Problem 12
গামাকিচি আর গামাতাতসু নামের দুটো ব্যাঙ যথাক্রমে \((0, 0)\) আর \((2, 0)\) বিন্দুতে আছে। তারা যথাক্রমে \((5, 5)\) আর \((7, 5)\) বিন্দুতে পৌঁছাতে চায়। তারা শুধু ধনাত্মক \(x\) বা \(y\) দিকে এক দৈর্ঘ্যের লাফ দিতে পারে। কতভাবে তারা তাদের লক্ষ্যে পৌঁছাতে পারবে যদি এমন কোনো বিন্দু না থাকে যেটা তারা দুজনই স...
- Sun Apr 11, 2021 9:38 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Secondary Problem 11
- Replies: 2
- Views: 3808
BdMO National 2021 Secondary Problem 11
\(ABCD\) এমন একটা বর্গ যেন \(A=(0, 0)\) এবং \(D=(1, 1)\)। \(P\left(\frac{2}{7},\frac{1}{4}\right)\) বর্গটার ভেতরে একটা বিন্দু। একটা পিঁপড়া \(P\) বিন্দু থেকে হাঁটা শুরু করে বর্গটার তিনটা বাহু স্পর্শ করার পর আবার \(P\) বিন্দুতে ফিরে আসে। পিঁপড়াটা দ্বারা সর্বনিম্ন সম্ভাব্য অতিক্রান্ত দূরত্বকে \(\frac...
- Sun Apr 11, 2021 9:36 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Secondary Problem 9
- Replies: 6
- Views: 8745
BdMO National 2021 Secondary Problem 9
Cynthia loves Pokemon and she wants to catch them all. In Victory Road, there are a total of $80$ Pokemon. Cynthia wants to catch as many of them as possible. However, she cannot catch any two Pokemon that are enemies with each other. After exploring around for a while, she makes the following two o...
- Sun Apr 11, 2021 7:35 pm
- Forum: Test Forum
- Topic: Can I delete this?
- Replies: 3
- Views: 7073
Re: Can I delete this?
This was a test. Why can't the author delete his own post?Asif Hossain wrote: ↑Sun Apr 11, 2021 7:06 pmnope you need to call moon bhai for this but unfortunately i think no moderator is active now tanmoy bhai comes rarely. You need to contact the moderator for this maybe
- Sun Apr 11, 2021 4:06 pm
- Forum: Social Lounge
- Topic: How was your national olympiad.
- Replies: 7
- Views: 8262
Re: How was your national olympiad.
Ami prothom prothom mone korsilam bhalo hoise. Pore problem gula akhane post deyar por @Pro_GRMR er solution gula dekhe depression e pore jacchi :cry: . Ebar mone hoy parbo na kichu korte. And ha chitkar amar onekkhon dhore korte chaileo korte pari ni. Kadte chaileo kadte parchi na. @Pro_GRMR moneh...
- Sun Apr 11, 2021 4:02 pm
- Forum: Test Forum
- Topic: Can I delete this?
- Replies: 3
- Views: 7073
Can I delete this?
Can I delete this?
- Sun Apr 11, 2021 3:58 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Secondary P4
- Replies: 1
- Views: 1879
Re: BdMO National 2021 Secondary P4
$ABCD$ be an isosceles trapezium such that $AD=BC$,$AB=6$ and $CD=8$. A point $E$ on the plane is such that $AE\perp EC$ and $BC=EC$. The length of $AE$ can be expressed as $a\sqrt{b}$ where $a$ and $b$ are integers and $b$ is not divisible by any square number other than $1$. Find the value of $(a...
- Sun Apr 11, 2021 3:44 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO Secondary National 2021 #7
- Replies: 1
- Views: 2544
Re: BDMO Secondary National 2021 #7
For a positive integer $n$ , let $s(n)$ and $c(n)$ be the number of divisors of $n$ that are perfect squares and perfect cubes respectively. A positive integer $n$ is called fair if $s(n)=c(n)>1$ . Find the number of fair integers less than $80$. Let $n$ be in prime factorized form $n= p_1^{e_1}p_2...