Search found 21 matches
- Wed Feb 20, 2019 2:37 am
- Forum: Divisional Math Olympiad
- Topic: BdMO Regional 2018 All question solved
- Replies: 1
- Views: 29298
Re: BdMO Regional 2018 All question solved
The document is updated. Here's the link https://drive.google.com/open?id=1zT77s ... -xHPN8201p
- Wed Mar 28, 2018 8:47 pm
- Forum: Geometry
- Topic: Measurement of small square
- Replies: 1
- Views: 8453
Re: Measurement of small square
can not see your screenshot
- Wed Mar 28, 2018 8:46 pm
- Forum: Geometry
- Topic: A hard Geometry Problem
- Replies: 4
- Views: 29696
Re: A hard Geometry Problem
Draw perpendicular from $O$ to $AB$ In $\triangle ABC$ $2\angle{ACB}=\angle{AOB}$ Again, in $\triangle {AOD}$ and $\triangle {DOB}$, $AO=OB$, and $\angle {ODA}=\angle{ODB}=90$ so $OD$ is angular bisector of $\angle{AOB}$ so $\angle{AOD}=\angle{ACB}$ so there complimentary angles are also same. so $\...
- Wed Mar 28, 2018 8:23 pm
- Forum: Secondary Level
- Topic: Triangle geometry
- Replies: 5
- Views: 6826
Re: Triangle geometry
i think it was 2017 BdMO regional qustion
- Wed Mar 28, 2018 8:18 pm
- Forum: Secondary Level
- Topic: Greatest Positive Integer $x$
- Replies: 7
- Views: 8096
Re: Greatest Positive Integer $x$
In $2000!$ there are $\lfloor {\frac{2000}{23}}\rfloor=86$ numbers which are divisible by $23$ and $\lfloor{{\frac{2000}{23^2}}}\rfloor=3$ numbers which are divisible by $23^2$ so $23^{89}||2000!$ so the answer would be $83$ it a a part of $Legendre's formula$ more information https://en.wikipedia.o...
- Wed Mar 28, 2018 8:04 pm
- Forum: Secondary Level
- Topic: BdMO 2017 Dhaka divitional
- Replies: 3
- Views: 12977
BdMO 2017 Dhaka divitional
For any rational numbers $x, y$ function $f(x)$ is a real number and $f(x+y)=f(x)f(y)-f(xy)+1$. Again $f(2017)\neq f(2018)$. $f(\frac{2017}{2018})=\frac{a}{b}$.Where $a,b$ are co-prime $a+b=?$
- Wed Mar 28, 2018 8:03 pm
- Forum: Secondary Level
- Topic: BdMO 2016 national
- Replies: 1
- Views: 4318
BdMO 2016 national
Juli is a mathematician and devised an algorithm to find a husband. The strategy is: • Start interviewing a maximum of $1000$ prospective husbands. Assign a ranking $r$ to each person that is a positive integer. No two prospects will have same the rank $r$. • Reject the first $k$ men and let $H$ be ...
- Wed Mar 28, 2018 8:02 pm
- Forum: Secondary Level
- Topic: BdMO 2017 Dhaka divitional
- Replies: 2
- Views: 5148
BdMO 2017 Dhaka divitional
The $‘energy’$ of an ordered triple $(a,b,c)$ formed by three positive integers $a,b,c$ is said to be $n$, if the following ${a}\leq{b}\leq{c}, gcd(a,b,c)=1$ and $(a^n+b^n+c^n)$ is divisible by $(a+b+c)$. There are some possible ordered triple whose $‘energy’$ can be of all values of ${n}\geq{1}$ In...
- Wed Mar 28, 2018 8:02 pm
- Forum: Divisional Math Olympiad
- Topic: BdMO 2017 Dhaka divitional
- Replies: 3
- Views: 9955
BdMO 2017 Dhaka divitional
Two points $A(x_A, y_B), B(x_A+5,y_B+12 )$ are on parabola $5x^2-px-5y+q=0$ such that $x_A+y_B=5$. How many possible positive integer pairs $(p, q)$ are there where positive integer $q \leq 2050$ ?
- Wed May 31, 2017 1:47 am
- Forum: Secondary Level
- Topic: Find $$(x,y)$$
- Replies: 4
- Views: 4461
Re: Find $$(x,y)$$
He just forgotten to give dollar . For him I am giving that..... The last part would be $ y=4k^2+5k+2 = 4k^2+5k+1+\frac{1}{2}+\frac{1}{2} \Rightarrow y^2 = (x^2 + \frac{x}{2} + \frac{1}{2} )^2 \Rightarrow x^4 + x^3 + x^2 + x + 1 = x^4 + x^3 + x^2 + \frac{x^2}{4} + \frac{x}{2} + \frac{1}{4} \Rightarr...