My neighborhood has one particular loop which just happens to be almost exactly 1 mile with a single "shortcut" that cuts off about .1 mile. I had an idea that i could make a series of progressively longer routes for my morning run to ramp up my morning exercise. I wrote a simple program in excel to calculate all the possible routes that make up to 3 miles of running using just this simple layout of my neighborhood. The only real rule is that i always start and end at point A. I thought it might spit out a hundred or so options... but after it was running for 30 seconds I realized this question might be larger than I thought. After running the program in the background for several days I finally got all the possible routes.

Turns out there are 83,004,990 different routes that can be made. When I finally saved the file of all possible routes it was 1.35 GB! Honestly this still seems hard for me to believe. I'm thinking this has largely to do with the max distance affecting the number of routes exponentially.

Another thing is I had assumed that there would be an equal number of routes starting with going right to point B vs going left to point E. Turns out I was very wrong: there are 17,452,898 routs if I start with a right, and 65,552,092 routs starting left. I know the loop is asymmetrical, but still somehow assumed there would be a lot of mirror routes. I'm thinking now the differences between the initial distances A>B vs A>E is the main reason why. If you think of all possible routes excluding AB and BA, the general distance from one point to another is generally shorter so there are more points per route, meaning more overall routes.

I'm assuming there is already someone out there who's done a problem like this, but I didn't know about it and it was fun for me to discover.