## Search found 1007 matches

Tue Nov 12, 2019 8:27 am
Topic: IMO 2019/P3
Replies: 5
Views: 59093

### Re: IMO 2019/P3

DAMN!!!!!!! This forum has got so dead... It needs a serious waking call... Maybe we should consider calling Thanos... to invade this forum. :twisted: Maybe then the "Avengers" (admins, moderators and former-active members) might turn their focus to this forum, again. :lol: (P.S: I don't know wheth...
Tue Nov 12, 2019 8:25 am
Forum: Combinatorics
Topic: Turkey TST 2014
Replies: 7
Views: 66247

### Re: Turkey TST 2014

Ragib Farhat Hasan wrote:
Tue Nov 05, 2019 12:57 am
BTW, I wonder...

This problem was posted over 5 years ago.

And no one posted a solution to this problem in half a decade!!! WOW!!!
Because there is no active member!
Tue Nov 12, 2019 8:17 am
Forum: Chemistry
Topic: Isobar
Replies: 2
Views: 55492

### Re: Isobar

Thu Aug 15, 2019 8:46 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P5
Replies: 0
Views: 81699

### APMO 2019 P5

Determine all the functions $f : \mathbb{R} \to \mathbb{R}$ such that
$f(x^2 + f(y)) = f(f(x)) + f(y^2) + 2f(xy)$for all real numbers $x$ and $y$.
Thu Aug 15, 2019 8:45 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P4
Replies: 0
Views: 69287

### APMO 2019 P4

Consider a $2018 \times 2019$ board with integers in each unit square. Two unit squares are said to be neighbours if they share a common edge. In each turn, you choose some unit squares. Then for each chosen unit square the average of all its neighbours is calculated. Finally, after these calculatio...
Thu Aug 15, 2019 8:44 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P3
Replies: 0
Views: 69867

### APMO 2019 P3

Let $ABC$ be a scalene triangle with circumcircle $\Gamma$. Let $M$ be the midpoint of $BC$. A variable point $P$ is selected in the line segment $AM$. The circumcircles of triangles $BPM$ and $CPM$ intersect $\Gamma$ again at points $D$ and $E$, respectively. The lines $DP$ and $EP$ intersect (a se...
Thu Aug 15, 2019 8:42 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P2
Replies: 0
Views: 57769

### APMO 2019 P2

Let $m$ be a fixed positive integer. The infinite sequence $\{a_n\}_{n\geq 1}$ is defined in the following way: $a_1$ is a positive integer, and for every integer $n\geq 1$ we have $$a_{n+1} = \begin{cases}a_n^2+2^m & \text{if } a_n< 2^m \\ a_n/2 &\text{if } a_n\geq 2^m\end{cases}$$For each $m$, det...
Thu Aug 15, 2019 8:41 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P1
Replies: 0
Views: 57667

### APMO 2019 P1

Let $\mathbb{Z}^+$ be the set of positive integers. Determine all functions $f : \mathbb{Z}^+\to\mathbb{Z}^+$ such that $a^2+f(a)f(b)$ is divisible by $f(a)+b$ for all positive integers $a,b$.
Thu May 16, 2019 10:40 am
Forum: Physics
Topic: BdPhO Regional (Dhaka-South) Higher Secondary 2019/2
Replies: 3
Views: 16758

### Re: BdPhO Regional (Dhaka-South) Higher Secondary 2019/2

SINAN EXPERT wrote:
Fri Apr 26, 2019 8:55 pm
Solution:
How did you draw this?
Thu May 16, 2019 10:37 am
Topic: BdMO National Secondary 2018:Full Solution
Replies: 2
Views: 15095

### Re: BdMO National Secondary 2018:Full Solution

SINAN EXPERT wrote:
Thu Apr 25, 2019 8:19 pm
samiul_samin wrote:
Mon Feb 25, 2019 1:45 pm
All solution of the problems of BdMO National Secondary $2018$ are available here.