[I'm new here so I am really not sure I'm in the right forum but it seems to be the closest thing to what I'm looking for. My apologies in advance if I'm wrong.]
It all started with a minor bug. I had a list of numbers to display followed by their sum. For example
Numbers: 1 57 23 - Sum: 81
The bug? I forgot the space between the numbers and it gave something like this
Numbers 15723 - Sum: 81
Being of a playful nature, I took it as a game and tried to retrieve the actual numbers based on their sum. I discussed it a bit with my Ph.D. supervisor. He never saw anything similar but thought it could be a NP-complete problem (with possibly some link to the set cover problem).
I got back to serious stuff and forgot about the whole thing. A couple of months ago, I thought again about this and decided to make a game out of it (link 1). However, I feel that this could be worth some academic investigation. So far, I know that when the splits are restricted to at most 2 digits, the number of combinations for a sequence of length n is Fn+1 (Fibonacci). Fibonacci is also the common thread in the mathematical formulas for all the other game variants (noise digits, reverse definition, etc.).
I'm not a maths scholar so I am not sure whether the whole thing is new or not. I've been posting in maths forums to find out. I posted almost verbatim the above text on Reddit (link 2). It was relatively well received (70-80%), generated 35+ comments, many of which were very insightful and well beyond my expectations. However, when it came to my core questions (novelty and NP-completeness), I could not get definite answers. So I'm posting here, hoping that I can get the attention of maths researchers.
Thanks in advance for your feedback
[To Moderators: if links are forbidden, please just cut what's below]