Search found 17 matches

by Enthurelxyz
Tue Apr 06, 2021 10:37 am
Forum: Combinatorics
Topic: Fires of planets of Phoenix
Replies: 1
Views: 92

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...
by Enthurelxyz
Thu Apr 01, 2021 12:53 pm
Forum: Combinatorics
Topic: The probability that Caitlin fought the dragon
Replies: 4
Views: 178

Re: The probability that Caitlin fought the dragon

Asif Hossain wrote:
Thu Apr 01, 2021 12:15 pm
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
off topic :
hmmm i see you are very competitve :roll:
Is it bad? :(
by Enthurelxyz
Wed Mar 31, 2021 11:17 am
Forum: Combinatorics
Topic: The probability that Caitlin fought the dragon
Replies: 4
Views: 178

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...
by Enthurelxyz
Tue Mar 30, 2021 2:33 pm
Forum: Junior Level
Topic: BDMO Regional Junior P8
Replies: 14
Views: 568

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,...
by Enthurelxyz
Tue Mar 30, 2021 2:32 pm
Forum: Junior Level
Topic: BDMO Regional Junior P8
Replies: 14
Views: 568

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 ...
by Enthurelxyz
Tue Mar 30, 2021 12:50 pm
Forum: Junior Level
Topic: BDMO Regional Junior P8
Replies: 14
Views: 568

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...
by Enthurelxyz
Sun Mar 28, 2021 9:22 am
Forum: Junior Level
Topic: BDMO Regional Junior P8
Replies: 14
Views: 568

BDMO Regional Junior P8

How many subsets of $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ contain $5$ consecutive numbers?
by Enthurelxyz
Thu Mar 11, 2021 10:22 am
Forum: Geometry
Topic: Construct a line through A
Replies: 1
Views: 380

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.
by Enthurelxyz
Thu Feb 25, 2021 7:15 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Junior 2020 P11
Replies: 1
Views: 338

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 ...
by Enthurelxyz
Tue Feb 09, 2021 8:21 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Junior 2020 P6
Replies: 2
Views: 402

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...