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Re: ABOUT HCl
Remember that in an aquas solution you already have $[H^+]=10^{-7}$. You can't make it less than that.
- Tue Feb 14, 2012 12:47 pm
- Forum: Algebra
- Topic: An inequality about sides of triangle
- Replies: 4
- Views: 3424
Re: An inequality about sides of triangle
BTW in case you guys haven't already checked it out-- Nayel bhai had written an awesome note on inequality http://www.kmcbd.org/Home/documents/Bas ... ects=0&d=1
- Sun Feb 12, 2012 10:18 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO 2012 National: Problem Sets
- Replies: 4
- Views: 44674
Re: BdMO 2012 National: Problem Sets
Thanks to Zzzz for LaTeXing and posting Primary and Junior problems.
- Sun Feb 12, 2012 9:22 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Higher Secondary 10
- Replies: 3
- Views: 4047
- Sun Feb 12, 2012 9:07 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Higher Secondary 09, Secondary 10
- Replies: 13
- Views: 23881
- Sat Feb 11, 2012 11:23 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Higher Secondary 10
- Replies: 3
- Views: 4047
BdMO National 2012: Higher Secondary 10
Problem 10: Consider a function $f: \mathbb{N}_0\to \mathbb{N}_0$ following the relations: $f(0)=0$ $f(np)=f(n)$ $f(n)=n+f\left ( \left \lfloor \dfrac{n}{p} \right \rfloor \right)$ when $n$ is not divisible by $p$ Here $p > 1$ is a positive integer, $\mathbb{N}_0$ is the set of all nonnegative inte...
- Sat Feb 11, 2012 11:23 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Higher Secondary 09, Secondary 10
- Replies: 13
- Views: 23881
BdMO National 2012: Higher Secondary 09, Secondary 10
Problem:
A triomino is an $L$-shaped pattern made from three unit squares. A $2^k \times 2^k$ chessboard has one of its squares missing. Show that the remaining board can be covered with triominoes.
A triomino is an $L$-shaped pattern made from three unit squares. A $2^k \times 2^k$ chessboard has one of its squares missing. Show that the remaining board can be covered with triominoes.
- Sat Feb 11, 2012 11:22 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Higher Secondary 08
- Replies: 4
- Views: 4494
BdMO National 2012: Higher Secondary 08
Problem 8: A decision making problem will be resolved by tossing $2n + 1$ coins. If Head comes in majority one option will be taken, for majority of tails it’ll be the other one. Initially all the coins were fair. A witty mathematician replaced $n$ pairs of fair coins with $n$ pairs of biased coins...
- Sat Feb 11, 2012 11:22 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Higher Secondary, Secondary 07
- Replies: 4
- Views: 4791
BdMO National 2012: Higher Secondary, Secondary 07
Problem:
In an acute angled triangle $ABC$, $\angle A= 60^0$. Prove that the bisector of one of the angles formed by the altitudes drawn from $B$ and $C$ passes through the center of the circumcircle of the triangle $ABC$.
In an acute angled triangle $ABC$, $\angle A= 60^0$. Prove that the bisector of one of the angles formed by the altitudes drawn from $B$ and $C$ passes through the center of the circumcircle of the triangle $ABC$.
- Sat Feb 11, 2012 11:22 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Higher Secondary, Secondary 06
- Replies: 5
- Views: 5407
BdMO National 2012: Higher Secondary, Secondary 06
Problem:
Show that for any prime $p$, there are either infinitely many or no positive integer $a$, so that $6p$ divides $a^p + 1$. Find all those primes for which there exists no solution.
Show that for any prime $p$, there are either infinitely many or no positive integer $a$, so that $6p$ divides $a^p + 1$. Find all those primes for which there exists no solution.