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

Answer 2

Answer: 35 is the most likely answer but 21 and 7 are also possible

Step-by-step explanation: well first of all, I have to say that the question was not clearly stated, he did not give the dimensions of the grid is it 1+6, 5+2 or 4+3  well of the sake of alexissaunders415 I am going to do all cases

for 1+6 lets solve it with the multiplication principle, 7!/6!1!=7 where do we get the 6!, well think about it, it can either go 6 up or 6 right, but the procedure up is repeated so we have to removed the choices that do not satisfy.

for 5+2 we do the same thing 7!/5!2!=21

then 4+3( the one I think he/she was asking about) 7!/4!3!=35