Pathing

StevenUnique

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Aug 27, 2021
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luigi lives 5 blocks west and 7 blocks north of his school(refer image) , how many unique path are there from his home to his school?IMG_20210828_025426.jpg
 
How many ways can the string [imath]SSSSSSSEEEEE[/imath] the rearranged ?
 
luigi lives 5 blocks west and 7 blocks north of his school(refer image) , how many unique path are there from his home to his school?View attachment 28674
Can go up left down right
Usually this sort of question asks for the number of paths of minimal length, which means in this case that you would only be going right and down; any time you go up you are wasting a "down".

If you remove that restriction, then there will be an infinite number of paths unless you have some other restriction, such as that you can't cross your path (that is, reuse any point). Do you intend "unique" to be such a restriction, or are you just using that to mean "distinct"?
 
Ok, how about the number of path with the maximum amount of notations without using the same road twice?
 
Ok, how about the number of path with the maximum amount of notations without using the same road twice?
In every case where such a question is given it is supposed that the steady-progress rule applies. In this case we move seven blocks south and five blocks east (that is known as the city-block or taxicab metric). Because the blocks can be traversed in any order the number of ways is [imath]\dfrac{12!}{(7!)(5!)}[/imath].
 
Ok, how about the number of path with the maximum amount of notations without using the same road twice?
What do you mean by "notations"? Do you mean, perhaps, that the path has to go through every intersection? Or that it has to have the greatest possible length without self-intersection?

You need to communicate your goal clearly, or it can't be solved. Are you making up the question as you go, or did it come from somewhere and you are trying to interpret it?
 
Ok, actually thinking about the it longer, I think the answer is infinite. I was thinking when i made this post I am gonna get a finite number like the Shannon number.
 
Hi Steven. I'm confused why you've ignored Dr. Peterson's questions.

What does "amount of notations" mean? Where did you see this exercise?

:confused:
 
Permutations Involving Identitical Object
By AlRichards34 on YOUTUBE.
From this at 5:01,I just changed the question a bit. When i saw the amount of route, I thought there can be more.

For example
R : right
L : left
U : up
D : down

RRRRRDDDDDDLDR
 
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