## The probability that Caitlin fought the dragon

For discussing Olympiad Level Combinatorics problems
Enthurelxyz
Posts: 17
Joined: Sat Dec 05, 2020 10:45 pm
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### 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 times, what is the probability that she has fought the dragon exactly once?

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

This is how I have approached.
and miles to go before we sleep
and miles to go before we sleep

Mehrab4226
Posts: 212
Joined: Sat Jan 11, 2020 1:38 pm

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

I used $12$ minutes to find this. There may be mistakes so sorry
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

Asif Hossain
Posts: 171
Joined: Sat Jan 02, 2021 9:28 pm

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

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
Hmm..Hammer...Treat everything as nail

Enthurelxyz
Posts: 17
Joined: Sat Dec 05, 2020 10:45 pm
Contact:

### 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
and miles to go before we sleep
and miles to go before we sleep

Asif Hossain
Posts: 171
Joined: Sat Jan 02, 2021 9:28 pm

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

Enthurelxyz wrote:
Thu Apr 01, 2021 12:53 pm
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