Question

Each square on the grid is 1 unit by 1 unit. You want to walk from point A to point B via a path that is 7 units long, but you have to stay on the grid. How many different paths can you take

Answer 1

Answer:

If you are traversing squares then 7 different paths can be taken

If you are traversing edges then 36 different paths can be taken

Step-by-step explanation:

I have attached a picture that would describe the grid which is 7 units long.

The solution to the general problem is if you have to take X right steps, and Y down steps then the number of routes is simply the ways of choosing where to take the down (or right) steps. Such that:

$\left (\ {X+Y} \atop {X}} \right.\left)=\left (\ {X+Y} \atop {Y}} \right.\left)$

Basically its the combination of terms.

In this problem,

If you are traversing squares then there are 6 right steps and 1 down step,

7 C 1 = 7 C 6= 7

If you are traversing edges then there are 7 right steps and 2 down steps:

9 C 2 = 9 C 7=  36