[whatshisface]

We do have a way of knowing this, it is as simple as saying that the finish line of a symbol game will stay the same given the initial symbols and the rules that can be used to move them around.

[thebooktocome]

OP is explicitly not talking about something open to human interaction (“saying”, “symbols”, “moving (symbols) around” are all human operations).

[whatshisface]

None of those are human-specific, machines and animals can do them. (Except saying, but I'm the one doing that verb, talking about moving symbols.)