My people.
https://urn.digitalarkivet.no/URN:NBN:no-a1450-rk10101508282...
and the output wasn't even recognizably Danish.
Just out of pity I gave it a birthday card from my sister written in very readable modern handwriting, and while in managed to make the contents of that readable, the errors it made reveals that it has very little contextual intelligence. Even if ! and ? can be hard to tell apart sometimes, they weren't here, and you do not usually start a birthday letter with "Happy Birthday brother?"
"The paradox is that this bot glut could eventually push most human interaction offline again; news (real news, that is) will be shared by talking, jobs will be found through connections, and friends will discover major life updates about one another at events and reunions. This is the best case. Another option is that we will have bot-free zones online."
"As more components of our lives become automated, we may want to give some extra thought to which of our routine human interactions are ok to reduce to a bot, and which are worth doing the old-fashioned way, with our own voices, hands, and eyes."
I read it. (I studied German in Primary School. I don't remember too much, but enough to skim the texts in Norwegian.) I'm also mathematician, so it's the kind of stuff I like. My guess is modulo 9 and then some bounds should explain most of it, but life is never so easy.
If you post the (auto)tranlated version and nobody gives an answer, I promise to try to solve it. (Obviously, I can't guarantee a solution.)
(In my experience, autotranlations does 90% of the job, but you need to polish it a little and in particular ensure the technical words are the correct ones.)
Title: Distribution of the Number of Steps to Kaprekar's Constant
We are trying Kaprekar's routine.
I choose a four-digit number with at least two different digits: 2345. We find the largest possible variant 5432 and the smallest possible variant 2345 from the digits and begin the routine...
5432 - 2345 = 3087 8730 - 0378 = 8352 8532 - 2358 = 6174
We have arrived at Kaprekar's constant: 6174 after 3 steps.
This is fine. If I now do this on all possible four-digit numbers, the number of steps required before 6174 is reached is distributed as follows:
The diagram showing the distribution of steps: https://earth.hoyd.net/wp-content/uploads/2025/03/kaprekars_...
This distribution seems a bit strange and not entirely intuitive. I immediately feel that the distribution should have been more evenly distributed.
Perhaps not evenly, but I think that one step to 6174 should be rarer than seven steps, shouldn't it? It has to do with the calculation i guess. There are a limited number of combinations where the result is 6174 on the first attempt. It feels a bit obvious and matches the diagram above. It slowly rises towards seven steps, is that to be expected?
What I find most strange is that three steps tops all others. Why is that? Why is there such a large presence of three? What does it mean? I would very much like to find an explanation for this.