Search found 9 matches
- Fri Apr 16, 2021 4:05 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Junior Problem 2
- Replies: 3
- Views: 5906
Re: BdMO National 2021 Junior Problem 2
My solution It can be easily observable that an equation where both side are sum of two number with same base but different power is not possible unless the base is $-1, 0, 1, 2$ So we will consider the powers are same. In the equation $5^{2r+1} + 5^{2} = 5^{r} + 5^{r+3}$ We will split the equation...
- Wed Apr 14, 2021 5:00 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Junior Problem 2
- Replies: 3
- Views: 5906
Re: BdMO National 2021 Junior Problem 2
$\begin{align*} &5^{2r+1}+5^2 = 5^r+5^{r+3} \\ \Longrightarrow & 5 \cdot (5^r)^2 + 25 = 5^r + 125 \cdot 5^r\\ \Longrightarrow & 5 \cdot (5^r)^2 + 25 = 126\cdot 5^r \\ \Longrightarrow & 5 \cdot (5^r)^2 - 126\cdot 5^r + 25 = 0 \\ \Longrightarrow & 5 \cdot (5^r)^2 -125\cdot 5^r -5^r + 25 = 0\\ \Longrig...
- Mon Apr 12, 2021 11:17 am
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO Secondary National 2021 #3
- Replies: 5
- Views: 7847
Re: BDMO Secondary National 2021 #3
It is considered in the solutionPritom12345 wrote: ↑Sun Apr 11, 2021 9:21 pmIsn't 125 a real number?
I mean it fulfills the condition:: [125] + {0} = 125.0 and there no condition like {r} != 0
so, why won't we add that number?
- Sat Apr 10, 2021 7:05 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO Secondary National 2021 #5
- Replies: 4
- Views: 3483
Re: BDMO Secondary National 2021 #5
the equation was $g(x) + g(y) = g(x+y) -xy$ :DMehrab4226 wrote: ↑Sat Apr 10, 2021 7:03 pmThank, you. Updated it.Pro_GRMR wrote: ↑Sat Apr 10, 2021 6:56 pmYou stated the question wrong.Mehrab4226 wrote: ↑Sat Apr 10, 2021 1:21 pm$g(x) : \mathbb{Z} \to \mathbb{Z}$ that satisfies
\[g(x)+y)=g(x)+g(y)-xy \]
If $g(x)=0$, what is the sum of all possible values of $g(35)$?
- Fri Apr 09, 2021 12:06 pm
- Forum: Secondary Level
- Topic: BdMO 2020 Secondary - Regional - P15
- Replies: 3
- Views: 58288
Re: BdMO 2020 Secondary - Regional - P15
Case 1: $a,b<200$ In ten's place, the order of the numbers matter, and we are limited to $9$ from $0$ as our sum. The ordered pairs for summation of $9$ is $(0,9), (1,8),...(4,5)$. In general, we can say that the number of ordered pairs for getting $a$ as sum is, $$\begin{align*} n(a) =\begin{cases...
- Thu Apr 08, 2021 1:07 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Geometry
- Replies: 2
- Views: 7882
Re: Geometry
$AB$, $AC$ and $BC$ are the vertices of a right angled triangle. Since $BD$ is the bisector of $\angle ABC$, $BC:AB = CD:AD = 1:2$. Thus $CD = 4$ and $AD = 6$. Using the Stewart's theorem, we have, $10(BD^2+4\cdot 6) = 2 \sqrt {5} \cdot 6 + 4 \sqrt{5}\cdot 4$. Solving this equation, we get $CE = BD ...
- Tue Apr 06, 2021 11:44 pm
- Forum: Site Support
- Topic: Can't update profile
- Replies: 4
- Views: 54802
Re: Can't update profile
It's fixed now. My settings didn't show those options before. :DMehrab4226 wrote: ↑Tue Apr 06, 2021 11:17 pmThis is how the user control panel in my laptop looks like. Yours should be the same too. If not try asking the admins or moderators like @Tanmoy bhaya.
Screenshot 2021-04-06 23.13.45.png
- Tue Apr 06, 2021 1:10 pm
- Forum: Site Support
- Topic: Can't update profile
- Replies: 4
- Views: 54802
Can't update profile
I can't find the option to add signature or update my profile(like adding interests, location or age). I have checked my user control panel but found nothing except adding an avatar.
- Tue Apr 06, 2021 12:02 pm
- Forum: Higher Secondary Level
- Topic: Pigeonhole Problem
- Replies: 14
- Views: 13748
Re: Pigeonhole Problem
This is my solution: $[1,55) = [1,1] U (1,2) U [2,3) U [3,5) U [5, 8) U [8,13) U [13,21) U [21,34) U [34,55)$ Now if we limit ourselves to picking one element from set at most, then we can have $n$ numbers such that no number satisfies $a+b>c$. But we have to pick $10$ numbers from $9$ sets and by P...