Question

Counting Question

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{The Red and Green lines are perpendicular to each other}\hspace{.33em}\\~\\
& \normalsize \text{Find the number of shortest paths to go from A to B.}\hspace{.33em}\\~\\
& \normalsize \text{Find the total number of paths to go from A to B.}\hspace{.33em}\\~\\
& \normalsize \text{(Assume the points are equidistant)}\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

You're welcom

Answer 3

I'm on iPad , cannot draw out the paths, b to me , there are 2 shortest ways , and their weight is 6

Answer 4

I will go look at my graph theory book and I am sure I will find something.

Answer 5

are u sure its 6

Answer 6

Go, diagonal fromA, 3 times, then go straight to B 3 more

Answer 7

there are algorithms for this, that would be a pain to teach on here.

google Dijkstra's algorithm

Answer 8

Assume each of the 6 red spaces have the same distance as the 3 green spaces,
Number of paths = 9!/(6!3!)=84 ways

Answer 9

diagonal?

Answer 10

along the lines, if the question was for me.

Answer 11

Djikistra algorithm finds shortest distance,

where as i need the number of shortest paths

Answer 12

Go to the right of A 1, then, diagonal, then right,then,diagonal,repeat 1 more time to get B

Answer 13

Use adjacent matrix to find them out. It works also

Answer 14

Why not diagonal? Since it is = right+ vertical up.?

Answer 15

answer is 210 for 1st one

Answer 16

the path has to along the lines can't jump diagonally

Answer 17

Ohoh, so I'm wrong, hehe.

Answer 18

an example

Answer 19

Yes that is right, there is some algorithm that will tell you.

Answer 20

It's like a permutation with 9 objects, 3 red and 6 green.
RGRGRGGGG
RRRGGGGGG
....
Using the multinomial theorem, the number of ways would be
9!/(6!3!)

Answer 21

thanks @mathmate ur anwers was correct

Answer 22

You're welcome! :)