What area of mathematics would the "24 game" encompass? [closed]

I'm doing an investigation on the 24 game and it's general solutions. However, as I'm still in high school, I don't know where to begin searching. Since the game deals with integers and how they can be composed by arithmetic operations, I am leaning towards concepts in number theory and combinatorics such as the compositions and partitions of a number. Still, I don't really feel satisfied with the help these concepts bring to my analysis.

Are there any fields of math that may describe the 24 game better? Maybe something like the composition of a number but with more operators?

I should note that there aren't many articles about the 24 game. Maybe it's too simple? Not well known?

As far as I know, games like this aren't of particular interest in research, I think because their constraints (i.e. which particular operations are allowed) don't arise naturally in theories that have broader applications.

It's helpful to ask specific questions about the game to focus your investigation. Instead of looking for ways to solve instances of the game, you might have success investigating how the existence of solutions (or the approximate number of solutions per instance) relates to the parameters of the problem. For example, with $n$ starting numbers instead of 4, which target values can be obtained and how are their sizes distributed? What's the approximate probability that the value $m$ can be obtained from $n$ initial numbers, as $n$ and $m$ grow large?

This could involve combinatorics (counting the expressions that can be formed) and computational analysis (writing a program to solve instances of the problem).