155667

I used trial and error to get 100.
I went first to find out the lowest number by going right then at the end of the maze go down and into the finish, which adds up to 37.
I then found out different ways but still at the beginning go right until the end of the maze. Doing this will not get 100.
I then tried going down at the beginning of the maze and right until I hit the wall, then down. I tried all these possibilities but I kept on getting lower than 100.
I then thought that because I wasnt getting high enough that I needed to add another loop to make a higher number. I then got 101 and 100.

From my workings of finding 100, I knew that 37 was the smallest possible number.

I also know from the finding 100, that it is 101.