## Search found 17 matches

- Tue Apr 06, 2021 10:37 am
- Forum: Combinatorics
- Topic: Fires of planets of Phoenix
- Replies:
**1** - Views:
**102**

### Fires of planets of Phoenix

In phoenix, a Galaxy far, far away, there are $2021$ planets. Define a $fire$ to be a path between two objects in phoenix. It is known that between every pair of planets either a single fire burns or no burning occurs. If we consider any subset of $2019$ planets, the total number of fires burning be...

- Thu Apr 01, 2021 12:53 pm
- Forum: Combinatorics
- Topic: The probability that Caitlin fought the dragon
- Replies:
**4** - Views:
**189**

### Re: The probability that Caitlin fought the dragon

Is it bad?Asif Hossain wrote: ↑Thu Apr 01, 2021 12:15 pmoff topic :Enthurelxyz wrote: ↑Wed Mar 31, 2021 11:17 am

Let do a thing: you'll try this problem for 20 minutes. If you can solve the problem then give the solution. If you can't, you can write how you have approached the problem for 20 minutes

hmmm i see you are very competitve

- Wed Mar 31, 2021 11:17 am
- Forum: Combinatorics
- Topic: The probability that Caitlin fought the dragon
- Replies:
**4** - Views:
**189**

### The probability that Caitlin fought the dragon

Caitlin is playing an game on a $3*3$ board. She starts her marker in the upper-lest square, and each turn she randomly chooses an adjacent square to move her marker to.(She can’t move diagonally.) If she moves to the center square, she fights the dragon. After Caitlin has moved her marker four time...

- Tue Mar 30, 2021 2:33 pm
- Forum: Junior Level
- Topic: BDMO Regional Junior P8
- Replies:
**14** - Views:
**615**

### Re: BDMO Regional Junior P8

User Mehrab4226 has already given the solution, though here I have shown a similar approach. Firstly, let's look at how many sets there are with $5$ elements that satisfy the question. It is easy to see there are five sets, namely $\{1, 2, 3, 4, 5\}, \{2, 3, 4, 5, 6\}, \{3, 4, 5, 6, 7\}, \{4, 5, 6,...

- Tue Mar 30, 2021 2:32 pm
- Forum: Junior Level
- Topic: BDMO Regional Junior P8
- Replies:
**14** - Views:
**615**

### Re: BDMO Regional Junior P8

Let us denote that kind of subsets as $X$ At first, we look at how many sets of $5$ consecutive numbers are there. 1.$\{1,2,3,4,5\}$ 2.$\{2,3,4,5,6\}$ 3.$\{3,4,5,6,7\}$ 4.$\{4,5,6,7,8\}$ 5.$\{5,6,7,8,9\}$ Now we will divide our work in $5$ cases. Case $1$ represents when number$ 1$. of the list is ...

- Tue Mar 30, 2021 12:50 pm
- Forum: Junior Level
- Topic: BDMO Regional Junior P8
- Replies:
**14** - Views:
**615**

### Re: BDMO Regional Junior P8

How many subsets of {1,2,3,4,5,6,7,8,9} contain $5$ consecutive numbers? Let us denote that kind of subsets as $X$ At first, we look at how many sets of $5$ consecutive numbers are there. 1.$\{1,2,3,4,5\}$ 2.$\{2,3,4,5,6\}$ 3.$\{3,4,5,6,7\}$ 4.$\{4,5,6,7,8\}$ 5.$\{5,6,7,8,9\}$ Now we will divide ou...

- Sun Mar 28, 2021 9:22 am
- Forum: Junior Level
- Topic: BDMO Regional Junior P8
- Replies:
**14** - Views:
**615**

### BDMO Regional Junior P8

How many subsets of $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ contain $5$ consecutive numbers?

- Thu Mar 11, 2021 10:22 am
- Forum: Geometry
- Topic: Construct a line through A
- Replies:
**1** - Views:
**401**

### Construct a line through A

Let $A$ be one of the common points of two intersecting circles. Through $A$ construct a line on which the two circles cut out equal chords.

- Thu Feb 25, 2021 7:15 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Junior 2020 P11
- Replies:
**1** - Views:
**346**

### Re: BdMO National Junior 2020 P11

Let, $n\neq 7$ So, $n \equiv 1,2,3,4,5,6 (mod$ $7)$ $ :arrow: $n^2 \equiv 1,2,4 (mod$ $7)$. If $n^2 \equiv 1 (mod$ $7)$ then $n ^2-8\equiv 0 (mod$ $7)$. So, $n^2=115$ but $15$ is not a perfect square. If $n^2\equiv 2 (mod$ $7)$ then $n^2-2=7 :arrow: n=3$ $but $3^2-8=1$ which is not a prime. If $n^2 ...

- Tue Feb 09, 2021 8:21 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Junior 2020 P6
- Replies:
**2** - Views:
**414**

### Re: BdMO National Junior 2020 P6

Draw two lines $l_1$ and $l_2$ on P such that they are perpendicular to $AD,BC$ and $AB,CD$ respectively. $l_1$ intersects $AD,BC$ at $E,F$ respectively and $l_2$ intersects $AB,CD$ at $G,H$ respectively. As, $\angle DAP = \angle DCP$ :arrow: $ \angle EAP=\angle HCP$ :arrow: $ \triangle AEP$ is simi...