forget about towns and distances. this is just a math problem dressed up in silly nonsense in an attempt to make it relatable, and it fails spectacularly

Not only clairvoyant, but also a necromancer! How cool is that!

What about the other 4 cheats you published? Were those accidents as well?

Can you tell me 2 raised to what power gives -2 ??

$ qalc -t 'log2(-2)'
1.000000000000000000000000000000000000000000000000000000000000000 + 4.532360141827193809627682945716666810171861467723795584186016548i

That is extremely confusing. No one would understand it that way.

To answer: "why does the second sequence you gave not fit the description of the kata?"

The sequence consists of repeatedly performing the given operation on the result of the previous operation, whereas you are performing some kind of string slicing with i on the same, initial string s.

e.g., using the Description example:

56789 # original input produces, after step 1:
 -> 67895 # output of the first operation, IS NOW THE INPUT FOR THE NEXT OPERATION
      # etc

.

Take the number of the example, pass it to your function, see the numbers you get, find what you're doing wrong.

56789 -> 67895 -> 68957 -> 68579 -> 68597 you should get these numbers
67895 -> 57896 -> 56897 -> 56798 -> 56789 you get these instead

Make a fork, add the tests you want.

.

Math.

I understand your point.
Consider the first list in the description: ls = [50, 55, 57, 58, 60].
In my thinking 50 is distance from a town A to a town B, 55 is d(B, C) and so on...
If they choose [57, 58, 60] they will drive from C to D, from D to E, from E to F.
If they choose [55, 58, 60] they will drive from B to C, from D to E, from E to F.
In the last case the story doesn't tell us how they go from C to D; it doesn't tell us how they go from home to B and from F to home but John doesn't drive.
Maybe they take a bike or a plane or whatever.
Our only problem is when John has to drive.

It is a failure to translate a simple abstract problem of ..., to a life problem.

Might be but many abstact problems come from life problem.
It was(is?) a habit at CW to "give" a story. This one doesn't seem to be really adequate but I am sure you have good ideas about how to improve or complete it.